Open Access
Translator Disclaimer
2008 Quantum characteristic classes and the Hofer metric
Yasha Savelyev
Geom. Topol. 12(4): 2277-2326 (2008). DOI: 10.2140/gt.2008.12.2277


Given a closed monotone symplectic manifold M, we define certain characteristic cohomology classes of the free loop space LHam(M,ω) with values in QH(M), and their S1 equivariant version. These classes generalize the Seidel representation and satisfy versions of the axioms for Chern classes. In particular there is a Whitney sum formula, which gives rise to a graded ring homomorphism from the ring H(ΩHam(M,ω),), with its Pontryagin product to QH2n+(M) with its quantum product. As an application we prove an extension to higher 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 circle action.


Download Citation

Yasha Savelyev. "Quantum characteristic classes and the Hofer metric." Geom. Topol. 12 (4) 2277 - 2326, 2008.


Received: 9 February 2008; Revised: 18 July 2008; Accepted: 5 June 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1146.53070
MathSciNet: MR2443967
Digital Object Identifier: 10.2140/gt.2008.12.2277

Primary: 53D45
Secondary: 22E67 , 53D35

Keywords: energy flow , Hamiltonian group , Hamiltonian symplectomorphism , Hofer metric , Loop group , quantum homology

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.12 • No. 4 • 2008
Back to Top