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Books on the topic 'Topological invariants'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 April 2025

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1

Szafraniec, Zbigniew. Topological invariants of real analytic sets. Gdańsk: Uniwersytet Gdański, 1993.

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2

Lipman, Joseph. Topological invariants of quasi-ordinary singularities. Providence, R.I., USA: American Mathematical Society, 1988.

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3

Kaminker, Jerome, ed. Geometric and Topological Invariants of Elliptic Operators. Providence, Rhode Island: American Mathematical Society, 1990. http://dx.doi.org/10.1090/conm/105.

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4

I, Arnolʹd V. Topological invariants of plane curves and caustics. Providence, R.I: American Mathematical Society, 1994.

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5

Prodan, Emil, and Hermann Schulz-Baldes. Bulk and Boundary Invariants for Complex Topological Insulators. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29351-6.

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6

Gabriel, Patrick. Ensemble d'invariants pour les produits croisés de Anzai. Montrouge, France: Société mathématique de France, 1991.

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7

Japan) RIMS Seminar "Twisted Topological Invariants and Topology of Low-dimensional Manifolds" (2010 September 13-17 Akita-ken. Twisted topological invariants and topology of low-dimensional manifolds: September 13-17, 2010. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2011.

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8

AMS-IMS-SIAM, Summer Research Conference on Conformal Field Theory Topological Field Theory and Quantum Groups (1992 Mount Holyoke College). Mathematical aspects of conformal and topological field theories and quantum groups. Providence, R.I: American Mathematical Society, 1994.

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9

Guadagnini, Enore. The link invariants of the Chern-Simons field theory: New developments in topological quantum field theory. Berlin: W. De Gruyter, 1993.

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10

Japan) RIMS Seminar "Representation Spaces Twisted Topological Invariants and Geometric Structures of 3-manifolds" (2012 May 28-June 1 Hakone-machi. Representation spaces twisted topological invariants and geometric structures of 3-manifolds: May 28-June 1, 2012. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2013.

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11

AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Geometric and Topological Invariants of Elliptic Operators (1988 Bowdoin College). Geometric and topological invariants of elliptic operators: Proceedings of the AMS-IMS-SIAM joint summer research conference held July 23-29, 1988 with support from the National Science Foundation and the U.S. Army Research Office. Edited by Kaminker Jerome, American Mathematical Society, Institute of Mathematical Statistics, and Society for Industrial and Applied Mathematics. Providence, R.I: American Mathematical Society, 1990.

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12

Konishi, Kukiko. Flop invariance of the topological vertex. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2006.

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13

Xu, Senlin. Jin dai wei fen ji he: Pu li lun yu deng pu wen ti, qu shuai yu tuo pu bu bian liang = Modern differential geometry : spectral theory and isospectrum problems, curvature and topological invariants. Hefei: Zhongguo ke xue ji shu da xue chu ban she, 2009.

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14

Kirchgraber, U. Geometry in the neighborhood of invariant manifolds of maps and flows and linearization. Harlow: Longman Scientific & Technical, 1990.

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15

Jaco, William H., Hyam Rubinstein, Craig David Hodgson, Martin Scharlemann, and Stephan Tillmann. Geometry and topology down under: A conference in honour of Hyam Rubinstein, July 11-22, 2011, The University of Melbourne, Parkville, Australia. Providence, Rhode Island: American Mathematical Society, 2013.

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16

Krzysztof, Jarosz, ed. Function spaces in modern analysis: Sixth Conference on Function Spaces, May 18-22, 2010, Southern Illinois University, Edwardsville. Providence, R.I: American Mathematical Society, 2011.

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17

Kloeden, Peter E. Nonautonomous dynamical systems. Providence, R.I: American Mathematical Society, 2011.

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18

Tretkoff, Paula. Topological Invariants and Differential Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0002.

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This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering spaces and some basics of the theory of complex manifolds and Hermitian metrics, including the concept of real manifold. Finally, it provides some general facts about divisors, line bundles, and the first Chern class on a complex manifold X.

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19

Topological Invariants of Stratified Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/3-540-38587-8.

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20

Topological Invariants of Stratified Spaces. Springer, 2007.

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21

Banagl, Markus. Topological Invariants of Stratified Spaces. Springer, 2010.

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22

Banagl, Markus. Topological Invariants of Stratified Spaces. Springer London, Limited, 2007.

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23

Fredholm Structures, topological invariants and applications. Springfield, MO: American Institute of Mathematical Sciences, 2009.

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24

McCarthy, John D. [from old catalog], and Selman Akbulut. Casson's Invariant for Oriented Homology Three-Spheres: An Exposition. Princeton University Press, 2014.

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25

McCarthy, John D. [from old catalog], and Selman Akbulut. Casson's Invariant for Oriented Homology Three-Spheres: An Exposition. Princeton University Press, 2014.

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26

Berlin, Freie Universität, ed. Topological quantum field theories and invariants of graphs. 1994.

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27

Broughan, K. A. Invariants for Real-Generated Uniform Topological and Algebraic Categories. Springer London, Limited, 2006.

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28

Snaith, Victor P. Topological Methods in Galois Representation Theory. Dover Publications, Incorporated, 2014.

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29

Snaith, Victor P. Topological Methods in Galois Representation Theory. Dover Publications, Incorporated, 2013.

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30

Snaith, Victor P. Topological Methods in Galois Representation Theory. Dover Publications, Incorporated, 2013.

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31

Vogt, R. M., and J. M. Boardman. Homotopy Invariant Algebraic Structures on Topological Spaces. Springer London, Limited, 2006.

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32

Quantum Superalgebras At Roots Of Unity Topological Invariants Of 3manifolds. VDM Verlag, 2008.

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33

John D. [from old catalog] McCarthy and Selman Akbulut. Casson's Invariant for Oriented Homology Three-Spheres: An Exposition. Princeton University Press, 2016.

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34

John D. [from old catalog] McCarthy and Selman Akbulut. Casson's Invariant for Oriented Homology Three-Spheres: An Exposition. Princeton University Press, 2014.

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35

Morgan, John W. Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44. Princeton University Press, 2014.

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36

Morgan, John W. Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. Princeton University Press, 2014.

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37

Prodan, Emil, and Hermann Schulz-Baldes. Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics. Springer, 2016.

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38

Prodan, Emil, and Hermann Schulz-Baldes. Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics. Springer, 2018.

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39

Prodan, Emil, and Hermann Schulz-Baldes. Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics. Springer, 2016.

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40

Topological Invariants of the Complement to Arrangements of Rational Plane Curves. American Mathematical Society, 2002.

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41

Functorial knot theory: Categories of tangles, coherence, categorical deformations, and topological invariants. Singapore: World Scientific, 2001.

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42

Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants. World Scientific Publishing Co Pte Ltd, 2001.

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43

Topological Invariants for Projection Method Patterns (Memoirs of the American Mathematical Society, No. 758). American Mathematical Society, 2002.

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44

Link Invariants of the Chern-Simons Field Theory: New Developments in Topological Quantum Field Theory. De Gruyter, Inc., 1993.

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45

Guadagnini, E. Link Invariants of the Chern-Simons Field Theory: New Developments in Topological Quantum Field Theory. de Gruyter GmbH, Walter, 2011.

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46

Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants. Series on Knots and Everything, Volume 26. World Scientific Publishing Co Pte Ltd, 2001.

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47

de Cataldo, Mark Andrea, Luca Migliorini Lectures 1–3, and Luca Migliorini. The Hodge Theory of Maps. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0005.

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This chapter summarizes the classical results of Hodge theory concerning algebraic maps. Hodge theory gives nontrivial restrictions on the topology of a nonsingular projective variety, or, more generally, of a compact Kähler manifold: the odd Betti numbers are even, the hard Lefschetz theorem, the formality theorem, stating that the real homotopy type of such a variety is, if simply connected, determined by the cohomology ring. Similarly, Hodge theory gives nontrivial topological constraints on algebraic maps. This chapter focuses on the latter, as it considers how the existence of an algebraic map f : X → Y of complex algebraic varieties is reflected in the topological invariants of X.

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48

Invarianti topologici e grammatiche universali. Acireale (Catania) [etc.]: Bonanno, 2006.

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49

Khoruzhenko, Boris, and Hans-Jurgen Sommers. Characteristic polynomials. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.19.

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This article considers characteristic polynomials and reviews a few useful results obtained in simple Gaussian models of random Hermitian matrices in the presence of an external matrix source. It first considers the products and ratio of characteristic polynomials before discussing the duality theorems for two different characteristic polynomials of Gaussian weights with external sources. It then describes the m-point correlation functions of the eigenvalues in the Gaussian unitary ensemble and how they are deduced from their Fourier transforms U(s1, … , sm). It also analyses the relation of the correlation function of the characteristic polynomials to the standard n-point correlation function using the replica and supersymmetric methods. Finally, it shows how the topological invariants of Riemann surfaces, such as the intersection numbers of the moduli space of curves, may be derived from averaged characteristic polynomials.

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50

Topology and geometry in dimension three: Triangulations, invariants, and geometric structures : conference in honor of William Jaco's 70th birthday, June 4-6, 2010, Oklahoma State University, Stillwater, OK. Providence, R.I: American Mathematical Society, 2011.

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