course: Floer homology and the heat flow

speaker: Joachim Weber (Ludwig-Maximilans-Universitat Munchen)

abstract: We study the heat flow in the loop space of a closed Riemannian manifold M as an adiabatic limit of the Floer equations in the cotangent bundle. This leads to a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the homology of the free loop space. As an application we prove, given a nontrivial free homotopy class of loops in the open unit disk cotangent bundle, existence of a 1-periodic orbit representing the class, for every compactly supported time-dependent Hamiltonian which is sufficiently large over the zero section.

timetable:
Wed 3 Nov, 11:00 - 12:00, Sala Conferenze Centro De Giorgi
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