Title: Gauged Floer Homology and Spectral Invariants
Abstract:We define a version of spectral invariant in the vortex Floer theory for a Hamiltonian |$G$|-manifold |$M$|. This defines potentially new (partial) symplectic quasimorphisms and quasistates when |$M/...We define a version of spectral invariant in the vortex Floer theory for a Hamiltonian |$G$|-manifold |$M$|. This defines potentially new (partial) symplectic quasimorphisms and quasistates when |$M/\kern-.7ex/ G$| is not semi-positive. Using a closed-open string map which connects the vortex Hamiltonian Floer homology of Guangbo Xu [37] to Woodward's quasimap Floer homology, the spectral invariant yields applications to non-displaceability problems of subsets in |$M/\kern-.7ex/ G$|.Read More