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 $M/\kern-.7ex/ G$ is not semi-positive. Using a closed-open string map which connects the vortex Ham...

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Bibliographic Details
Published in:International mathematics research notices 2018-07, Vol.2018 (13), p.3959-4021
Main Authors: Wu, Weiwei, Xu, Guangbo
Format: Article
Language:English
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Summary: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 $M/\kern-.7ex/ G$ 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 $M/\kern-.7ex/ G$.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnx005