Relevant bibliographies by topics / Morse-Bott theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Morse-Bott theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Morse-Bott theory"

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Hutchings, Michael, and Jo Nelson. "Axiomatic S1 Morse–Bott theory." Algebraic & Geometric Topology 20, no. 4 (2020): 1641–90. http://dx.doi.org/10.2140/agt.2020.20.1641.

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CASASAYAS, J., J. MARTINEZ ALFARO, and A. NUNES. "KNOTS AND LINKS IN INTEGRABLE HAMILTONIAN SYSTEMS." Journal of Knot Theory and Its Ramifications 07, no. 02 (1998): 123–53. http://dx.doi.org/10.1142/s0218216598000097.

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The main purpose of this paper is to prove that Bott integrable Hamiltonian flows and non-singular Morse-Smale flows are closely related. As a consequence, we obtain a classification of the knots and links formed by periodic orbits of Bott integrable Hamiltonians on the 3-sphere and on the solid torus. We also show that most of Fomenko's theory on the topology of the energy levels of Bott integrable Hamiltonians can be derived from Morgan's results on 3-manifolds that admit non-singular Morse-Smale flows.
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HURTUBISE, DAVID E. "MULTICOMPLEXES AND SPECTRAL SEQUENCES." Journal of Algebra and Its Applications 09, no. 04 (2010): 519–30. http://dx.doi.org/10.1142/s0219498810004087.

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In this note, we present some algebraic examples of multicomplexes whose differentials differ from those in the spectral sequences associated to the multicomplexes. The motivation for constructing examples showing the algebraic distinction between a multicomplex and its associated spectral sequence comes from the author's work on Morse–Bott homology with A. Banyaga [A. Banyaga and D. E. Hurtubise, Morse–Bott homology, Trans. Amer. Math. Soc. (to appear), arXiv:math/0612316v2].
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Lima, D. V. S., O. Manzoli Neto, and K. A. de Rezende. "On handle theory for Morse–Bott critical manifolds." Geometriae Dedicata 202, no. 1 (2018): 265–309. http://dx.doi.org/10.1007/s10711-018-0413-7.

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Scáardua, Bruno, and José Seade. "Codimension one foliations with Bott-Morse singularities I." Journal of Differential Geometry 83, no. 1 (2009): 189–212. http://dx.doi.org/10.4310/jdg/1253804355.

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OH, YONG-GEUN, and RUI WANG. "ANALYSIS OF CONTACT CAUCHY–RIEMANN MAPS II: CANONICAL NEIGHBORHOODS AND EXPONENTIAL CONVERGENCE FOR THE MORSE–BOTT CASE." Nagoya Mathematical Journal 231 (May 15, 2017): 128–223. http://dx.doi.org/10.1017/nmj.2017.17.

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This is a sequel to the papers Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43–63, eds. by Y.-J. Suh and et al. for ICM-2014 satellite conference, Daejeon, Korea, August 2014; arXiv:1212.4817; Analysis of contact Cauchy–Riemann maps I: a priori$C^{k}$estimates and asymptotic convergence, submitted, preprint, 2012, arXiv:1212.5186v3). In Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43–63, eds. by Y.-J. Suh and et al. for ICM-2014 satellite conference, Daejeon, Korea, Augus
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Albers, Peter, and Doris Hein. "Cuplength estimates in Morse cohomology." Journal of Topology and Analysis 08, no. 02 (2016): 243–72. http://dx.doi.org/10.1142/s1793525316500102.

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The main goal of this paper is to give a unified treatment to many known cuplength estimates with a view towards Floer theory. As the base case, we prove that for [Formula: see text]-perturbations of a function which is Morse–Bott along a closed submanifold, the number of critical points is bounded below in terms of the cuplength of that critical submanifold. As we work with rather general assumptions the proof also applies in a variety of Floer settings. For example, this proves lower bounds (some of which were known) for the number of fixed points of Hamiltonian diffeomorphisms, Hamiltonian
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Savelyev, Yasha. "Yang–Mills theory and jumping curves." International Journal of Mathematics 26, no. 05 (2015): 1550029. http://dx.doi.org/10.1142/s0129167x15500299.

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We study a smooth analogue of jumping curves of a holomorphic vector bundle, and use Yang–Mills theory over S2 to show that any non-trivial, smooth Hermitian vector bundle E over a smooth simply connected manifold, must have such curves. This is used to give new examples complex manifolds for which a non-trivial holomorphic vector bundle must have jumping curves in the classical sense (when c1(E) is zero). We also use this to give a new proof of a theorem of Gromov on the norm of curvature of unitary connections, and make the theorem slightly sharper. Lastly we define a sequence of new non-tri
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Rochon, Frédéric. "Rigidity of Hamiltonian Actions." Canadian Mathematical Bulletin 46, no. 2 (2003): 277–90. http://dx.doi.org/10.4153/cmb-2003-028-7.

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AbstractThis paper studies the following question: Given an ω′-symplectic action of a Lie group on a manifoldMwhich coincides, as a smooth action, with a Hamiltonian ω-action, when is this action a Hamiltonian ω′-action? Using a result of Morse-Bott theory presented in Section 2, we show in Section 3 of this paper that such an action is in fact a Hamiltonian ω′-action, provided thatM is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In
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Feehan, Paul M. N., and Manousos Maridakis. "Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (2020): 35–67. http://dx.doi.org/10.1515/crelle-2019-0029.

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AbstractWe prove several abstract versions of the Łojasiewicz–Simon gradient inequality for an analytic function on a Banach space that generalize previous abstract versions of this inequality, weakening their hypotheses and, in particular, that of the well-known infinite-dimensional version of the gradient inequality due to Łojasiewicz [S. Łojasiewicz, Ensembles semi-analytiques, (1965), Publ. Inst. Hautes Etudes Sci., Bures-sur-Yvette. LaTeX version by M. Coste, August 29, 2006 based on mimeographed course notes by S. Łojasiewicz, https://perso.univ-rennes1.fr/michel.coste/Lojasiewicz.pdf] a
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Dissertations / Theses on the topic "Morse-Bott theory"

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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
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Mennesson, Pierre. "Homologie symplectique Tⁿ-équivariante pour les variétés toriques hamiltoniennes". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS315/document.

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Cette thèse établit l'existence d'une variante de l'homologie de Floer de type Morse-Bott. Étant donnés une variété torique (W²ⁿ, ω, µ) et un hamiltonien H : W × S ¹ → ℝ invariant par l’action du tore de dimension n Tⁿ, , les orbites de H sont stables par l’action torique. Cette dernière admettant des points fixes dans W, elle n’est pas libre, pareillement pour celle induit sur les lacets de W et il est, a priori, impossible de construire une théorie de Morse-Bott équivariante au niveau de C∞(S¹, W)/Tⁿ. Nous remédions à ce problème en adoptant la construction de Borel : nous choisissons un esp
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Heistercamp, Muriel. "The Weinstein conjecture with multiplicities on spherizations." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209882.

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Soit M une variété lisse fermée et considérons sont fibré cotangent T*M muni de la structure symplectique usuelle induite par la forme de Liouville. Une hypersurface S de T*M$ est dite étoilée fibre par fibre si pour tout point q de M, l'intersection Sq de S avec la fibre au dessus de q est le bord d'un domaine étoilé par rapport à l'origine 0q de la fibre T*qM. Un flot est naturellement associé à S, il s'agit de l'unique flot généré par le champ de Reeb le long de S, le flot de Reeb. <p><p>L'existence d'une orbite orbite fermée du flot de Reeb sur S fut annoncée par Weinstein dans sa conjectu
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Yaptieu, Djeungue Odette Sylvia. "Generalizations of discrete Morse theory." 2017. https://ul.qucosa.de/id/qucosa%3A17104.

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We generalize Forman’s discrete Morse theory, on one end by developing a discrete analogue of Morse-Bott theory for CW complexes, motivated by Morse-Bott theory in the smooth setting. On the other, motivated by J-N. Corvellec’s Morse theory for continuous functionals, we generalize Forman’s discrete Morse-floer theory by considering a vector field more general than the one extracted from a discrete Morse function, and defining a boundary operator from which the Betti numbers of the CW complex are obtained. We also do some Conley theory analysis.
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Books on the topic "Morse-Bott theory"

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Mimura, M. Topology of lie groups, I and II. American Mathematical Society, 1991.

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Book chapters on the topic "Morse-Bott theory"

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Austin, D. M., and P. J. Braam. "Morse-Bott theory and equivariant cohomology." In The Floer Memorial Volume. Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9217-9_8.

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Bott, Raoul. "Morse Theory Indomitable." In Raoul Bott Collected Papers. Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-2564-5_19.

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Bott, Raoul. "Morse Theoretic Aspects of Yang-Mills Theory." In Raoul Bott Collected Papers. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2564-5_5.

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Bott, Raoul. "An Equivariant Setting of the Morse Theory." In Raoul Bott Collected Papers. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2564-5_6.

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Bott, Raoul. "Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces." In Raoul Bott Collected Papers. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2564-5_4.

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"The Bott-Morse theory." In Translations of Mathematical Monographs. American Mathematical Society, 2000. http://dx.doi.org/10.1090/mmono/091/09.

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