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Equivariant Lagrangian Floer cohomology via semi-global Kuranishi structures

Erkao Bao and Ko Honda
Algebraic & Geometric Topology 21 (2021) 1677–1722
DOI: 10.2140/agt.2021.21.1677
Abstract

Using a simplified version of Kuranishi perturbation theory, which we call semi-global Kuranishi structures, we give a definition of the equivariant Lagrangian Floer cohomology of a pair of Lagrangian submanifolds that are fixed under a finite symplectic group action and satisfy certain simplifying assumptions.

Keywords
equivariant Lagrangian Floer homology, semi-global Kuranishi structure, relative spin, coherent orientation, symplectic structure
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53D10, 53D40
References
Publication
Received: 3 May 2019
Revised: 1 May 2020
Accepted: 28 July 2020
Published: 18 August 2021
Authors
Erkao Bao
School of Mathematics
University of Minnesota
Minneapolis, MN
United States
Ko Honda
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA
United States
http://www.math.ucla.edu/~honda