Journal of Symplectic Geometry

Three approaches towards Floer homology of cotangent bundles

Joa Weber

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 1 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1154467633

Mathematical Reviews number (MathSciNet)
MR2235858

Zentralblatt MATH identifier
1109.53080

Citation

Weber, Joa. Three approaches towards Floer homology of cotangent bundles. J. Symplectic Geom. 3 (2005), no. 4, 671--701. https://projecteuclid.org/euclid.jsg/1154467633


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