Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems

Details Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems

2010-08-11

arxiv.org/abs/1008.1852v1

Mathematics

Symplectic Geometry

30 pages, 0 figures

Scientific paper

The objective of this note is to prove the existence result for brake orbits in classical Hamiltonian systems (which is first proved by Bolotin) by using Floer theory. To this end, we compute an open string analogue of symplectic homology (so called wrapped Floer homology) of some domains in cotangent bundles, which appear naturally in study of classical Hamiltonian systems. The main part of the computations is to show invariance of wrapped Floer homology under certain handle attaching to domains.

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