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dc.contributorMiranda Galcerán, Eva
dc.contributorOms, Cedric
dc.contributor.authorBrugués Mora, Joaquim
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractMorse homology studies the topology of smooth manifolds by examining the critical points of a real-valued function defined on the manifold, and connecting them with the negative gradient of the function. Rather surprisingly, the resulting homology is proved to be independent of the choice of the real-valued function and metric defining the negative gradient. This leads to a topological lower bound on the number of critical points. In the 1980s, the construction of Morse homology served as a prototype to define a homology spanned by $1$-periodic Hamiltonian diffeomorphisms on symplectic manifolds. The resulting homology, introduced by Andreas Floer, spectacularly revolutionized the area of symplectic topology and leaded to a proof of the famous Arnold conjecture. Floer theory still is the subject of a lot of active and exciting research and is nowadays an essential technique in symplectic topology.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject.lcshSymplectic geometry
dc.subject.otherMorse theory
dc.subject.otherFloer theory
dc.subject.otherPeriodic orbits
dc.subject.otherFixed points
dc.subject.otherArnold conjecture
dc.titleMorse theory and Floer homology
dc.typeMaster thesis
dc.subject.lemacGeometria simplèctica
dc.subject.amsClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

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