Geometry & Topology
- Geom. Topol.
- Volume 12, Number 4 (2008), 2277-2326.
Quantum characteristic classes and the Hofer metric
Given a closed monotone symplectic manifold , we define certain characteristic cohomology classes of the free loop space with values in , and their 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 , with its Pontryagin product to with its quantum product. As an application we prove an extension to higher dimensional geometry of the loop space of a theorem of McDuff and Slimowitz on minimality in the Hofer metric of a semifree Hamiltonian circle action.
Geom. Topol., Volume 12, Number 4 (2008), 2277-2326.
Received: 9 February 2008
Revised: 18 July 2008
Accepted: 5 June 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]
Savelyev, Yasha. Quantum characteristic classes and the Hofer metric. Geom. Topol. 12 (2008), no. 4, 2277--2326. doi:10.2140/gt.2008.12.2277. https://projecteuclid.org/euclid.gt/1513800127