Journal of Symplectic Geometry

Three approaches towards Floer homology of cotangent bundles

Joa Weber

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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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J. Symplectic Geom., Volume 3, Number 4 (2005), 671-701.

First available in Project Euclid: 1 August 2006

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Weber, Joa. Three approaches towards Floer homology of cotangent bundles. J. Symplectic Geom. 3 (2005), no. 4, 671--701.

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