Relevant bibliographies by topics / Morse theory; Donaldson's theorem

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
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Academic literature on the topic 'Morse theory; Donaldson's theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Morse theory; Donaldson's theorem"

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Harvey, F. R., and H. B. Lawson. "Morse theory and Stokes’ theorem." Surveys in Differential Geometry 7, no. 1 (2002): 259–311. http://dx.doi.org/10.4310/sdg.2002.v7.n1.a9.

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Greene, Joshua Evan. "A note on applications of the d-invariant and Donaldson's theorem." Journal of Knot Theory and Its Ramifications 26, no. 02 (February 2017): 1740006. http://dx.doi.org/10.1142/s0218216517400065.

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This paper contains two remarks about the application of the [Formula: see text]-invariant in Heegaard Floer homology and Donaldson's diagonalization theorem to knot theory. The first is the equivalence of two obstructions they give to a 2-bridge knot being smoothly slice. The second carries out a suggestion by Stefan Friedl to replace the use of Heegaard Floer homology by Donaldson's theorem in the proof of the main result of [J. E. Greene, Lattices, graphs, and Conway mutation, Invent. Math. 192(3) (2013) 717–750] concerning Conway mutation of alternating links.
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Martynchuk, N., H. W. Broer, and K. Efstathiou. "Hamiltonian Monodromy and Morse Theory." Communications in Mathematical Physics 375, no. 2 (October 1, 2019): 1373–92. http://dx.doi.org/10.1007/s00220-019-03578-2.

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Abstract We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the system. Our proof is based on Takens’s index theorem, which specifies how the energy-h Chern number changes when h passes a non-degenerate critical value, and a choice of admissible cycles in Fomenko–Zieschang theory. Connections of our result to some of the existing approaches to monodromy are discussed.
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Kukieła, Michał. "The main theorem of discrete Morse theory for Morse matchings with finitely many rays." Topology and its Applications 160, no. 9 (June 2013): 1074–82. http://dx.doi.org/10.1016/j.topol.2013.04.025.

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Sakkalis, Takis. "On a theorem of H. Hopf." International Journal of Mathematics and Mathematical Sciences 13, no. 4 (1990): 813–16. http://dx.doi.org/10.1155/s0161171290001132.

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Fischer, Arthur E. "Riemannian submersions and the regular interval theorem of Morse theory." Annals of Global Analysis and Geometry 14, no. 3 (August 1996): 263–300. http://dx.doi.org/10.1007/bf00054474.

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DUAN, YI-SHI, and PENG-MING ZHANG. "INNER STRUCTURE OF GAUSS–BONNET–CHERN THEOREM AND THE MORSE THEORY." Modern Physics Letters A 16, no. 39 (December 21, 2001): 2483–93. http://dx.doi.org/10.1142/s0217732301006004.

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We define a new one-form HA based on the second fundamental tensor [Formula: see text], the Gauss–Bonnet–Chern form can be novelly expressed with this one-form. Using the ϕ-mapping theory we find that the Gauss–Bonnet–Chern density can be expressed in terms of the δ-function δ(ϕ) and the relationship between the Gauss–Bonnet–Chern theorem and Hopf–Poincaré theorem is given straightforwardly. The topological current of the Gauss–Bonnet–Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.
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Razvan, M. R. "On Conley's fundamental theorem of dynamical systems." International Journal of Mathematics and Mathematical Sciences 2004, no. 26 (2004): 1397–401. http://dx.doi.org/10.1155/s0161171204202125.

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Wilkin, Graeme. "Equivariant Morse Theory for the Norm-Square of a Moment Map on a Variety." International Mathematics Research Notices 2019, no. 15 (November 18, 2017): 4730–63. http://dx.doi.org/10.1093/imrn/rnx286.

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AbstractWe show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow around the critical sets is well-behaved, and the singular space must satisfy a local deformation retract condition. We then show that these conditions are satisfied when the function is the norm-square of a moment map on an affine variety, and that the homotopy equivalence from this theorem is equivariant with respect to the associated Hamiltonian group action. An important special case of these results is that the main theorem of Morse theory holds for the norm square of a moment map on the space of representations of a finite quiver with relations.
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Johnson, Lacey, and Kevin Knudson. "Min-Max Theory for Cell Complexes." Algebra Colloquium 27, no. 03 (August 27, 2020): 447–54. http://dx.doi.org/10.1142/s100538672000036x.

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In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. We introduce a discretized version of this theory associated to a discrete Morse function on a (regular) cell complex. As applications we prove a discrete version of the mountain pass lemma and give an alternate proof of a discrete Lusternik–Schnirelmann theorem.
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Dissertations / Theses on the topic "Morse theory; Donaldson's theorem"

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Frøyshov, Kim A. "On Floer homology and four-manifolds with boundary." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282194.

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Bonatto, Luciana Basualdo. "Bott\'s periodicity theorem from the algebraic topology viewpoint." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-17112017-130250/.

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In 1970, Raoul Bott published The Periodicity Theorem for the Classical Groups and Some of Its Applications, in which he uses this famous result as a guideline to present some important areas and tools of Algebraic Topology. This dissertation aims to use the path Bott presented in his article as a guideline to address certain topics on Algebraic Topology. We start this incursion developing important tools used in Homotopy Theory such as spectral sequences and Eilenberg-MacLane spaces, exploring how they can be combined to aid in computation of homotopy groups. We then study important results of Morse Theory, a tool which was in the centre of Botts proof of the Periodicity Theorem. We also develop two extensions: Morse-Bott Theory, and the applications of such results to the loopspace of a manifold. We end by giving an introduction to generalised cohomology theories and K-Theory.
Em 1970, Raoul Bott publicou o artigo The Periodicity Theorem for the Classical Groups and Some of Its Applications no qual usava esse famoso resultado como um guia para apresentar importantes áreas e ferramentas da Topologia Algébrica. O presente trabalho usa o mesmo caminho traçado por Bott em seu artigo como roteiro para explorar tópicos importantes da Topologia Algébrica. Começamos esta incursão desenvolvendo ferramentas importantes da Teoria de Homotopia como sequências espectrais e espaços de Eilenberg-MacLane, explorando como estes podem ser combinados para auxiliar em cálculos de grupos de homotopia. Passamos então a estudar resultados importantes de Teoria de Morse, uma ferramenta que estava no centro da demonstração de Bott do Teorema da Periodicidade. Desenvolvemos ainda, duas extensões: Teoria de Morse-Bott e aplicações destes resultados ao espaço de laços de uma variedade. Terminamos com uma introdução a teorias de cohomologia generalizadas e K-Teoria.
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Lapébie, Julie. "Sur la topologie des ensembles semi-algébriques : caractéristique d'Euler; degré topologique et indice radial." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4719/document.

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Suite aux travaux de Zbigniew Szafraniec et Nicolas Dutertre, je me suis intéressée aux calculs de caractéristiques d'Euler de certains espaces semi-algébriques. En particulier, ceux de laforme : $ {(-1)^{varepsilon_1} G_1geq 0 }cap...cap{(-1)^{varepsilon_l} G_lgeq 0}cap W$, où $epsilon=(epsilon_1,...,epsilon_l)in{0,1}^l$, $G=(G_1,...,G_l):R^nrightarrowR^l$ polynomiale et $W:=F^{-1}(0)subsetR^n$ où $F:R^nrightarrowR^k$ et $k+lleq n$. Une fois le cas lisse traité, on intersecte ces ensembles avec ${ fgeq 0}$ ou ${ fleq 0}$, où $f$ est polynomiale telle que $f^{-1}(0)$ admette un nombre fini de singularités. J'énonce alors un théorème reliant ces caractéristiques au degré d'applications faisant intervenir les fonctions $f$, $F$ et $G$. Pour finir, on s'intéresse au cas où l'ensemble $W$ possède un lieu critique compact.Dans une autre partie, je travaille sur l'indice radial, indice défini sur des variétés singulières. J'énonce un résultat faisant le lien entre l'indice radial d'un champ de vecteurs V en une singularité avec l'indice radial de son opposé -V. Finalement, je relie l'indice radial à un indice d'intersection
After the works of Zbigniew Szafraniec and Nicolas Dutertre, we are interested in computing Euler characteristics of some particular semialgebraic sets. In particular, the ones of the form : $ {(-1)^{varepsilon_1} G_1geq 0 }cap...cap{(-1)^{varepsilon_l} G_lgeq 0}cap W$, where $varepsilon=(varepsilon_1,...,varepsilon_l)in{0,1}^l$, $G=(G_1,...,G_l):R^nrightarrowR^l$ polynomial and $W:=F^{-1}(0)subsetR^n$ where $F:R^nrightarrowR^k$ and $k+lleq n$. Once the smooth case is treated, we intersect these sets with ${ fgeq 0}$ or ${ fleq 0}$, where $f$ is polynomial such that $f^{-1}(0)$ contains a finite number of singularities. Then we state a theorem that makes a link between these caracteristics and some degrees of mappings involving the functions $f$, $F$ and $G$. Finally, we study the case where $W$ has a compact singular set.In another part, I work with the radial index, an index defined for singular manifolds. I have a result making a link between the radial index of a vector field V and its opposite -V at a singularity. Finally, I relate that radial index to an intersection index
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Lee, Jung-Hsuan, and 李容瑄. "Morse Theory to Reeb''s Theorem and its Generalization." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/38936612442251708008.

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碩士
淡江大學
數學學系碩士班
101
In this thesis, we want to use Morse Theorem to prove Reeb''s Theorem. Before showing the proof of these theorems, we need to review some basic properties of a differentiable manifold M with a differentiable structure. In general, if we define some functions from M (or its subspace) to real value, the difference between manifold and coordinate space should be considered. Every point we choose must send to a coordinate subspace first. So defining a coordinate system is helpful to deal with any functions on manifold M. The main result we review is to prove Reeb''s Theorem using Morse Lemma and Morse Theorem. Here we use a surgery lemma to prove disjoint union of two spaces, matched along their common boundary. We also show how to construct a homotopy equivalence between manifold M and a n-sphere, for all dimension n is larger or equal to 1.
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St-Pierre, Alexandre. "Homologie de morse et théorème de la signature." Thèse, 2009. http://hdl.handle.net/1866/7892.

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Waterstraat, Nils. "The Index Bundle for Gap-Continuous Families, Morse-Type Index Theorems and Bifurcation." Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-0006-B3F1-1.

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Books on the topic "Morse theory; Donaldson's theorem"

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Bismut, Jean-Michel. An extension of a theorem by Cheeger and Müller. Montrouge: Société mathématique de France, 1992.

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Garner, Robert. The Contemporary Debate in Animal Ethics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199375967.003.0019.

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This final chapter explores the range of ideas current in the contemporary animal ethics debate. Much of the chapter is devoted to documenting the critique of the animal welfare ethic, which holds that, while animals have moral standing, humans, being persons, have a superior moral status. Three different strands of this critique—based on utilitarian, rights, and contractarian approaches—are identified and explored. The final part of the chapter documents the fragmentation of the animal ethics debate in recent years. This has included a more nuanced position which seeks to decouple animal rights from abolitionism, accounts of animal ethics from virtue ethics and capabilities perspectives, and a relational turn associated with the feminist care ethic tradition and, more recently, the utilization of citizenship theory by Donaldson and Kymlicka.
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Book chapters on the topic "Morse theory; Donaldson's theorem"

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Goresky, Mark, and Robert MacPherson. "Proof of the Main Theorem." In Stratified Morse Theory, 100–113. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-71714-7_10.

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Goresky, Mark, and Robert MacPherson. "Dramatis Personae and the Main Theorem." In Stratified Morse Theory, 60–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-71714-7_5.

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Goresky, Mark, and Robert MacPherson. "The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theorem." In Stratified Morse Theory, 23–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-71714-7_2.

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Karhumäki, Juhani, Aleksi Saarela, and Luca Q. Zamboni. "Variations of the Morse-Hedlund Theorem for k-Abelian Equivalence." In Developments in Language Theory, 203–14. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09698-8_18.

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Behrens, Stefan, Allison N. Miller, Matthias Nagel, and Peter Teichner. "The Schoenflies Theorem after Mazur, Morse, and Brown." In The Disc Embedding Theorem, 44–62. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198841319.003.0003.

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‘The Schoenflies Theorem after Mazur, Morse, and Brown’ provides two proofs of the Schoenflies theorem. The Schoenflies theorem states that every bicollared embedding of an (n – 1)-sphere in the n-sphere splits the n-sphere into two balls. This chapter provides two proofs. The first is due to Mazur and Morse; it utilizes an infinite ‘swindle’ and a classical technique called push-pull. The second proof, due to Brown, serves as an introduction to shrinking, or decomposition space theory. The latter is a beautiful, but outmoded, branch of topology that can be used to produce non-differentiable homeomorphisms between manifolds, especially from a manifold to a quotient space. Techniques from decomposition space theory are essential in the proof of the disc embedding theorem.
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Niekerk, Mathilda van, and Donald Getz. "Perspectives on Stakeholder Theory." In Event Stakeholders. Goodfellow Publishers, 2019. http://dx.doi.org/10.23912/9781911396635-4089.

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This chapter provides elaboration of stakeholder theory, commencing with four general perspectives on stakeholder theory as identified by Donaldson and Preston (1995). This is followed by a discussion of how CSR or corporate social responsibility has influenced thinking about stakeholders and forms an integral part of the normative perspective. Carroll’s (1993) popular CSR model has been adapted and modified for this book, providing a more integrated and relevant approach. Defining and classifying stakeholders is the third major topic covered, drawing first on generic stakeholder theory and commencing with a discussion of primary and secondary, active and passive stakeholders. Particularly attention is given to the framework provided by Mitchell, Agle and Wood (1997) that defines ‘stockholder salience’ as a combination of ‘legitimacy, power and urgency’. These terms are explored in detail. The chapter concludes with an examination of event and tourism stakeholders, including a diagram and research notes from the events and tourism literature.
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Almanza, German, Victor M. Carrillo, and Cely C. Ronquillo. "Optimization of Utility Functions in an Admissible Space of Higher Dimension." In Handbook of Research on Military, Aeronautical, and Maritime Logistics and Operations, 102–13. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9779-9.ch006.

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S. Smale published a paper where announce a theorem which optimize a several utility functions at once (cf. Smale, 1975) using Morse Theory, this is a very abstract subject that require high skills in Differential Topology and Algebraic Topology. Our goal in this paper is announce the same theorems in terms of Calculus of Manifolds and Linear Algebra, those subjects are more reachable to engineers and economists whom are concern with maximizing functions in several variables. Moreover, the elements involved in our theorems are accessible to graduate students, also we putting forward the results we consider economically relevant.
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