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December 2005 Three approaches towards Floer homology of cotangent bundles
Joa Weber
J. Symplectic Geom. 3(4): 671-701 (December 2005).


Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow, for instance, quadratically in the fibers outside a compact set, one can define Floer homology and show that it is naturally isomorphic to singular homology of the free loop space. We review the three isomorphisms constructed by Viterbo [16], Salamon--Weber [18] and Abbondandolo--Schwarz [14]. The theory is illustrated by calculating Morse and Floer homology in case of the Euclidean \textit{n}-torus. Applications include existence of noncontractible periodic orbits of compactly supported Hamiltonians on open unit disc cotangent bundles which are sufficiently large over the zero section.


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Joa Weber. "Three approaches towards Floer homology of cotangent bundles." J. Symplectic Geom. 3 (4) 671 - 701, December 2005.


Published: December 2005
First available in Project Euclid: 1 August 2006

zbMATH: 1109.53080
MathSciNet: MR2235858

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 4 • December 2005
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