Quantum characteristic classes and the Hofer metric

Content Provider	Semantic Scholar
Author	Avelyev, Y. Asha S.
Copyright Year	2009
Abstract	Given a closed monotone symplectic manifold M , we define certain characteristic cohomology classes of the free loop space LHam(M, ω) with values inQH∗(M), and theirS1 equivariant version. These classes generalize the Seidel r pr sentation and satisfy versions of the axioms for Chern classes. In part icular there is a Whitney sum formula, which gives rise to a graded ring homomo rphism from the ringH∗(ΩHam(M, ω),Q), with its Pontryagin product toQH2n+∗(M) with its quantum product. As an application we prove an extension to h igher dimensional geometry of the loop space LHam(M, ω) of a theorem of McDuff and Slimowitz on minimality in the Hofer metric of a semifree Hamiltonian c ircle action.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/0709.4510v3.pdf
Language	English
Access Restriction	Open
Subject Keyword	Class Delta operator Hamiltonian (quantum mechanics) Quantum Symplectic integrator Version manifold monotone
Content Type	Text
Resource Type	Article