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Journal articles on the topic 'Nonorientable Surfaces'

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Author: Grafiati

Published: 19 October 2024

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1

Bujalance, J. A., and B. Estrada. "q-hyperelliptic compact nonorientable Klein surfaces without boundary." International Journal of Mathematics and Mathematical Sciences 31, no. 4 (2002): 215–27. http://dx.doi.org/10.1155/s0161171202109173.

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LetXbe a nonorientable Klein surface (KS in short), that is a compact nonorientable surface with a dianalytic structure defined on it. A Klein surfaceXis said to beq-hyperellipticif and only if there exists an involutionΦonX(a dianalytic homeomorphism of order two) such that the quotientX/〈Φ〉has algebraic genusq.q-hyperelliptic nonorientable KSs without boundary (nonorientable Riemann surfaces) were characterized by means of non-Euclidean crystallographic groups. In this paper, using that characterization, we determine bounds for the order of the automorphism group of a nonorientableq-hyperelliptic Klein surfaceXsuch thatX/〈Φ〉has no boundary and prove that the bounds are attained. Besides, we obtain the dimension of the Teichmüller space associated to this type of surfaces.

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2

NAKAZAWA, NAOHITO. "ON FIELD THEORIES OF LOOPS." Modern Physics Letters A 10, no. 29 (September 21, 1995): 2175–84. http://dx.doi.org/10.1142/s0217732395002337.

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We apply stochastic quantization method to real symmetric matrix models for the second quantization of nonorientable loops in both discretized and continuum levels. The stochastic process defined by the Langevin equation in loop space describes the time evolution of the nonorientable loops defined on nonorientable 2-D surfaces. The corresponding Fokker-Planck Hamiltonian deduces a nonorientable string field theory at the continuum limit.

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3

Danthony, Claude, and Arnaldo Nogueira. "Measured foliations on nonorientable surfaces." Annales scientifiques de l'École normale supérieure 23, no. 3 (1990): 469–94. http://dx.doi.org/10.24033/asens.1608.

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4

Stukow, Michał. "Dehn twists on nonorientable surfaces." Fundamenta Mathematicae 189, no. 2 (2006): 117–47. http://dx.doi.org/10.4064/fm189-2-3.

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5

Hartsfield, Nora, and Gerhard Ringel. "Minimal quadrangulations of nonorientable surfaces." Journal of Combinatorial Theory, Series A 50, no. 2 (March 1989): 186–95. http://dx.doi.org/10.1016/0097-3165(89)90014-9.

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6

YURTTAŞ, Saadet Öykü, and Mehmetcik PAMUK. "Integral laminations on nonorientable surfaces." TURKISH JOURNAL OF MATHEMATICS 42 (2018): 69–82. http://dx.doi.org/10.3906/mat-1608-76.

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7

Levine, Adam, Daniel Ruberman, and Sašo Strle. "Nonorientable surfaces in homology cobordisms." Geometry & Topology 19, no. 1 (February 27, 2015): 439–94. http://dx.doi.org/10.2140/gt.2015.19.439.

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8

Barza, Ilie, and Dorin Ghisa. "Vector fields on nonorientable surfaces." International Journal of Mathematics and Mathematical Sciences 2003, no. 3 (2003): 133–52. http://dx.doi.org/10.1155/s0161171203204038.

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A one-to-one correspondence is established between the germs of functions and tangent vectors on a NOSXand the bi-germs of functions, respectively, elementary fields of tangent vectors (EFTV) on the orientable double cover ofX. Some representation theorems for the algebra of germs of functions, the tangent space at an arbitrary point ofX, and the space of vector fields onXare proved by using a symmetrisation process. An example related to the normal derivative on the border of the Möbius strip supports the nontriviality of the concepts introduced in this paper.

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9

Friesen, Tyler, and Vassily Olegovich Manturov. "Checkerboard embeddings of *-graphs into nonorientable surfaces." Journal of Knot Theory and Its Ramifications 23, no. 07 (June 2014): 1460004. http://dx.doi.org/10.1142/s0218216514600049.

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This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of nonorientable surfaces into which such graphs may be embedded. In a previous paper [Embeddings of *-graphs into 2-surfaces, preprint (2012), arXiv:1212.5646] by the authors, the problem of calculating whether a given *-graph in which all vertices have degree 4 or 6 admits a ℤ2-homologically trivial embedding into a given orientable surface was shown to be equivalent to a problem on matrices. Here we extend those results to nonorientable surfaces. The embeddability condition that we obtain yields quadratic-time algorithms to determine whether a *-graph with all vertices of degree 4 or 6 admits a ℤ2-homologically trivial embedding into the projective plane or into the Klein bottle.

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10

L�pez, Francisco J., and Francisco Mart�n. "Complete nonorientable minimal surfaces and symmetries." Duke Mathematical Journal 79, no. 3 (September 1995): 667–86. http://dx.doi.org/10.1215/s0012-7094-95-07917-4.

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11

Lu, Wentao T., and F. Y. Wu. "Close-packed dimers on nonorientable surfaces." Physics Letters A 293, no. 5-6 (February 2002): 235–46. http://dx.doi.org/10.1016/s0375-9601(02)00019-1.

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12

Ross, Marty. "Complete nonorientable minimal surfaces in R3." Commentarii Mathematici Helvetici 67, no. 1 (December 1992): 64–76. http://dx.doi.org/10.1007/bf02566489.

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13

Archdeacon, Dan, and Phil Huneke. "A Kuratowski theorem for nonorientable surfaces." Journal of Combinatorial Theory, Series B 46, no. 2 (April 1989): 173–231. http://dx.doi.org/10.1016/0095-8956(89)90043-9.

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14

Ho, Nan-Kuo, and Chiu-Chu Melissa Liu. "Yang-Mills connections on nonorientable surfaces." Communications in Analysis and Geometry 16, no. 3 (2008): 617–79. http://dx.doi.org/10.4310/cag.2008.v16.n3.a6.

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15

Atalan, F., and E. Medetogullari. "The Birman-Hilden property of covering spaces of nonorientable surfaces." Ukrains’kyi Matematychnyi Zhurnal 72, no. 3 (March 28, 2020): 307–15. http://dx.doi.org/10.37863/umzh.v72i3.6044.

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16

Parlak, Anna, and Michał Stukow. "Roots of Dehn twists on nonorientable surfaces." Journal of Knot Theory and Its Ramifications 28, no. 12 (October 2019): 1950077. http://dx.doi.org/10.1142/s0218216519500779.

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Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist [Formula: see text] about a nonseparating circle [Formula: see text] in the mapping class group [Formula: see text] of a nonorientable surface [Formula: see text] of genus [Formula: see text]. We explore the existence of roots and, following the work of McCullough, Rajeevsarathy and Monden, give a simple arithmetic description of their conjugacy classes. We also study roots of maximal degree and prove that if we fix an odd integer [Formula: see text], then for each sufficiently large [Formula: see text], [Formula: see text] has a root of degree [Formula: see text] in [Formula: see text]. Moreover, for any possible degree [Formula: see text], we provide explicit expressions for a particular type of roots of Dehn twists about nonseparating circles in [Formula: see text].

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17

Atalan, Ferihe, and Mustafa Korkmaz. "Automorphisms of curve complexes on nonorientable surfaces." Groups, Geometry, and Dynamics 8, no. 1 (2014): 39–68. http://dx.doi.org/10.4171/ggd/216.

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18

Dai, Bo, Chung-I. Ho, and Tian-Jun Li. "Nonorientable Lagrangian surfaces in rational 4–manifolds." Algebraic & Geometric Topology 19, no. 6 (October 20, 2019): 2837–54. http://dx.doi.org/10.2140/agt.2019.19.2837.

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19

Ginés Espín Buendía, José, Daniel Peralta-salas, and Gabriel Soler López. "Existence of minimal flows on nonorientable surfaces." Discrete & Continuous Dynamical Systems - A 37, no. 8 (2017): 4191–211. http://dx.doi.org/10.3934/dcds.2017178.

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20

Ishihara, Toru. "Complete Nonorientable Minimal Surfaces in R 3." Transactions of the American Mathematical Society 333, no. 2 (October 1992): 889. http://dx.doi.org/10.2307/2154069.

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21

Bujalance, J. A. "Hyperelliptic compact nonorientable Klein surfaces without boundary." Kodai Mathematical Journal 12, no. 1 (1989): 1–8. http://dx.doi.org/10.2996/kmj/1138038984.

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22

Machon, T., and G. P. Alexander. "Knots and nonorientable surfaces in chiral nematics." Proceedings of the National Academy of Sciences 110, no. 35 (August 12, 2013): 14174–79. http://dx.doi.org/10.1073/pnas.1308225110.

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23

Karimipour, V., and A. Mostafazadeh. "Lattice topological field theory on nonorientable surfaces." Journal of Mathematical Physics 38, no. 1 (January 1997): 49–66. http://dx.doi.org/10.1063/1.531830.

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24

de Oliveira, M. Elisa G. G. "Some new examples of nonorientable minimal surfaces." Proceedings of the American Mathematical Society 98, no. 4 (April 1, 1986): 629. http://dx.doi.org/10.1090/s0002-9939-1986-0861765-0.

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25

Gabai, David, and William H. Kazez. "The classification of maps of nonorientable surfaces." Mathematische Annalen 281, no. 4 (December 1988): 687–702. http://dx.doi.org/10.1007/bf01456845.

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26

ATALAN, FERIHE. "OUTER AUTOMORPHISMS OF MAPPING CLASS GROUPS OF NONORIENTABLE SURFACES." International Journal of Algebra and Computation 20, no. 03 (May 2010): 437–56. http://dx.doi.org/10.1142/s0218196710005716.

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27

OZAWA, MAKOTO. "ESSENTIAL STATE SURFACES FOR KNOTS AND LINKS." Journal of the Australian Mathematical Society 91, no. 3 (December 2011): 391–404. http://dx.doi.org/10.1017/s1446788712000055.

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AbstractWe study a canonical spanning surface obtained from a knot or link diagram, depending on a given Kauffman state. We give a sufficient condition for the surface to be essential. By using the essential surface, we can deduce the triviality and splittability of a knot or link from its diagrams. This has been done on the extended knot or link class that includes all semiadequate, homogeneous knots and links, and most algebraic knots and links. In order to prove the main theorem, we extend Gabai’s Murasugi sum theorem to the case of nonorientable spanning surfaces.

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28

Gromadzki, Grzegorz. "Supersoluble Groups of Automorphisms of Nonorientable Riemann Surfaces." Bulletin of the London Mathematical Society 22, no. 6 (November 1990): 561–68. http://dx.doi.org/10.1112/blms/22.6.561.

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29

Solov’eva, F. I. "Tilings of nonorientable surfaces by Steiner triple systems." Problems of Information Transmission 43, no. 3 (September 2007): 213–24. http://dx.doi.org/10.1134/s0032946007030040.

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30

Li, Youlin, and Burak Ozbagci. "Fillings of unit cotangent bundles of nonorientable surfaces." Bulletin of the London Mathematical Society 50, no. 1 (October 26, 2017): 7–16. http://dx.doi.org/10.1112/blms.12104.

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31

Lu, Wentao T., and F. Y. Wu. "Erratum to: “Close-packed dimers on nonorientable surfaces”." Physics Letters A 298, no. 4 (June 2002): 293. http://dx.doi.org/10.1016/s0375-9601(02)00518-2.

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32

Tzeng, W. J., and F. Y. Wu. "Spanning trees on hypercubic lattices and nonorientable surfaces." Applied Mathematics Letters 13, no. 7 (October 2000): 19–25. http://dx.doi.org/10.1016/s0893-9659(00)00071-9.

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33

Bernatzki, Felicia. "The Plateau-Douglas problem for nonorientable minimal surfaces." manuscripta mathematica 79, no. 1 (December 1993): 73–80. http://dx.doi.org/10.1007/bf02568329.

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34

Ho, Nan-Kuo, and Chiu-Chu Liu. "Yang-Mills connections on orientable and nonorientable surfaces." Memoirs of the American Mathematical Society 202, no. 948 (2009): 0. http://dx.doi.org/10.1090/s0065-9266-09-00564-x.

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35

Meeks, III, William H. "Regularity of the Albanese map for nonorientable surfaces." Journal of Differential Geometry 29, no. 2 (1989): 345–52. http://dx.doi.org/10.4310/jdg/1214442878.

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36

Ho, Nan-Kuo, Chiu-Chu Melissa Liu, and Daniel Ramras. "Orientability in Yang–Mills theory over nonorientable surfaces." Communications in Analysis and Geometry 17, no. 5 (2009): 903–53. http://dx.doi.org/10.4310/cag.2009.v17.n5.a3.

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37

Alarcón, Antonio, and Francisco J. López. "Approximation theory for nonorientable minimal surfaces and applications." Geometry & Topology 19, no. 2 (April 10, 2015): 1015–62. http://dx.doi.org/10.2140/gt.2015.19.1015.

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38

Aranson, S. Kh, E. V. Zhuzhoma, and I. A. Tel'nykh. "Transitive and supertransitive flows on closed nonorientable surfaces." Mathematical Notes 63, no. 4 (April 1998): 549–52. http://dx.doi.org/10.1007/bf02311259.

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39

Nicholls, Sarah Ruth, Nancy Scherich, and Julia Shneidman. "Large 1-systems of curves in nonorientable surfaces." Involve, a Journal of Mathematics 16, no. 1 (April 14, 2023): 127–39. http://dx.doi.org/10.2140/involve.2023.16.127.

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40

ALI, FATEMA, and FERIHE ATALAN. "CONNECTEDNESS OF THE CUT SYSTEM COMPLEX ON NONORIENTABLE SURFACES." Kragujevac Journal of Mathematics 46, no. 1 (February 2022): 21–28. http://dx.doi.org/10.46793/kgjmat2201.021a.

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Let N be a compact, connected, nonorientable surface of genus g with n boundary components. In this note, we show that the cut system complex of N is connected for g < 4 and disconnected for g ≥ 4. We then deﬁne a related complex and show that it is connected for g ≥ 4.

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41

Eudave-Muñoz, Mario, and José Frías. "The Neuwirth Conjecture for a family of satellite knots." Journal of Knot Theory and Its Ramifications 28, no. 02 (February 2019): 1950017. http://dx.doi.org/10.1142/s0218216519500172.

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Let [Formula: see text] be a nontrivial knot in [Formula: see text]. It was conjectured that there exists a Neuwirth surface for [Formula: see text]. That is, a closed surface in [Formula: see text] containing the knot [Formula: see text] as a nonseparating curve and such that every compressing disk for the surface intersects the knot in at least two points. We provide explicit constructions of Neuwirth surfaces for a family of satellite knots, which do not depend on the existence of nonorientable algebraically incompressible and [Formula: see text]-incompressible spanning surfaces for these knots.

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42

KORKMAZ, MUSTAFA. "First homology group of mapping class groups of nonorientable surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 123, no. 3 (May 1998): 487–99. http://dx.doi.org/10.1017/s0305004197002454.

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Recall that the first homology group H1(G) of a group G is the derived quotient G/[G, G]. The first homology groups of the mapping class groups of closed orientable surfaces are well known. Let F be a closed orientable surface of genus g. Recall that the extended mapping class group [Mscr ]*F of the surface F is the group of the isotopy classes of self-homeomorphisms of F. The mapping class group [Mscr ]F of F is the subgroup of [Mscr ]*F consisting of the isotopy classes of orientation-preserving self-homeomorphisms of F. It is well known that [Mscr ]F is trivial if F is a sphere. Hence the first homology group of the mapping class group of a sphere is trivial. If the genus of F is at least three, then H1([Mscr ]F) is again trivial. This result is due to Powell [P]. The group H1([Mscr ]F) is Z10 if the genus of F is two, proved by Mumford [Mu], and Z12 if F is a torus. When a problem about orientable surfaces is solved, it is natural to ask the corresponding problem for nonorientable surfaces. This is our motivation for the present paper.

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43

Petrenjuk, V. I., and D. A. Petrenjuk. "About Structure of Graph Obstructions for Klein Surface with 9 Vertices." Cybernetics and Computer Technologies, no. 4 (December 31, 2020): 65–86. http://dx.doi.org/10.34229/2707-451x.20.4.5.

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The structure of the 9 vertex obstructive graphs for the nonorientable surface of the genus 2 is established by the method of j-transformations of the graphs. The problem of establishing the structural properties of 9 vertex obstruction graphs for the surface of the undirected genus 2 by the method of j-transformation of graphs is considered. The article has an introduction and 5 sections. The introduction contains the main definitions, which are illustrated, to some extent, in Section 1, which provides several statements about their properties. Sections 2 – 4 investigate the structural properties of 9 vertex obstruction graphs for an undirected surface by presenting as a j-image of several graphs homeomorphic to one of the Kuratovsky graphs and at least one planar or projective-planar graph. Section 5 contains a new version of the proof of the statement about the peculiarities of the minimal embeddings of finite graphs in nonorientable surfaces, namely, that, in contrast to oriented surfaces, cell boundaries do not contain repeated edges. Also in section 5 the other properties peculiar to embeddings of graphs to non-oriented surfaces and the main result are given. The main result is Theorem 1. Each obstruction graph H for a non-oriented surface N2 of genus 2 satisfies the following. 1. An arbitrary edge u,u = (a,b) is placed on the Mebius strip by some minimal embedding of the graph H in N3 and there exists a locally projective-planar subgraph K of the graph H \ u which satisfies the condition: (tK({a,b},N3)=1)˄(tK\u({a,b},N2)=2), where tK({a,b},N) is the number of reachability of the set {a,b} on the nonorientable surface N; 2. There exists the smallest inclusion of many different subgraphs Ki of a 2-connected graph H homeomorphic to the graph K+e, where K is a locally planar subgraph of the graph H (at least K+e is homemorphic to K5 or K3,3), which covers the set of edges of the graph H. Keywords: graph, Klein surface, graph structure, graph obstruction, non-oriented surface, Möbius strip.

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44

Ho, Nan-Kuo, and Chiu-Chu Melissa Liu. "On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces." Canadian Journal of Mathematics 56, no. 6 (December 1, 2004): 1228–36. http://dx.doi.org/10.4153/cjm-2004-053-3.

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AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

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45

Khorrami, M., and M. Alimohammadi. "Observables of the Generalized 2D Yang–Mills Theories on Arbitrary Surfaces: A Path Integral Approach." Modern Physics Letters A 12, no. 30 (September 28, 1997): 2265–70. http://dx.doi.org/10.1142/s0217732397002338.

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Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2-D Yang–Mills theories in the Schwinger–Fock gauge. Our calculation is done for arbitrary 2-D orientable, and also nonorientable surfaces.

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46

Gromadzki, G. "On soluble groups of automorphisms of nonorientable Klein surfaces." Fundamenta Mathematicae 141, no. 3 (1992): 215–27. http://dx.doi.org/10.4064/fm-141-3-215-227.

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47

Ishihara, Tōru. "Harmonic maps of nonorientable surfaces to four-dimensional manifolds." Tohoku Mathematical Journal 45, no. 1 (1993): 1–12. http://dx.doi.org/10.2748/tmj/1178225951.

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48

Fujimori, Shoichi, and Francisco J. López. "Nonorientable maximal surfaces in the Lorentz-Minkowski 3-space." Tohoku Mathematical Journal 62, no. 3 (2010): 311–28. http://dx.doi.org/10.2748/tmj/1287148614.

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49

Davies, James, and Florian Pfender. "Edge‐maximal graphs on orientable and some nonorientable surfaces." Journal of Graph Theory 98, no. 3 (July 6, 2021): 405–25. http://dx.doi.org/10.1002/jgt.22705.

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50

Martín, Francisco, and Francisco J. Lopez. "Complete nonorientable minimal surfaces with the highest symmetry group." American Journal of Mathematics 119, no. 1 (1997): 55–81. http://dx.doi.org/10.1353/ajm.1997.0004.

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