Finite group actions on lagrangian floer theory

Cheol Hyun Cho, Hansol Hong

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We construct finite group actions on Lagrangian Floer theory when symplectic manifolds have finite group actions and Lagrangian submanifolds have induced group actions. We first define finite group actions on Novikov-Morse theory. We introduce the notion of a spin profile as an obstruction class of extending the group action on Lagrangian submanifold to the one on its spin structure, which is a group cohomology class in H2(G; Z/2). For a class of Lagrangian submanifolds which have the same spin profiles, we define a finite group action on their Fukaya category. In consequence, we obtain the s-equivariant Fukaya category as well as the s-orbifolded Fukaya category for each group cohomology class s. We also develop a version with G-equivariant bundles on Lagrangian submanifolds, and explain how character group of G acts on the theory. As an application, we define an orbifolded Fukaya-Seidel category of a G-invariant Lefschetz fibration, and also discuss homological mirror symmetry conjectures with group actions.

Original languageEnglish
Pages (from-to)307-420
Number of pages114
JournalJournal of Symplectic Geometry
Volume15
Issue number2
DOIs
Publication statusPublished - 2017 Jan 1

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Finite Group Action
Lagrangian Submanifold
Group Action
Group Cohomology
Equivariant
Lefschetz Fibration
Spin Structure
Mirror Symmetry
Morse Theory
Symplectic Manifold
Obstruction
Bundle
Invariant
Class
Profile

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Cho, Cheol Hyun ; Hong, Hansol. / Finite group actions on lagrangian floer theory. In: Journal of Symplectic Geometry. 2017 ; Vol. 15, No. 2. pp. 307-420.
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Finite group actions on lagrangian floer theory. / Cho, Cheol Hyun; Hong, Hansol.

In: Journal of Symplectic Geometry, Vol. 15, No. 2, 01.01.2017, p. 307-420.

Research output: Contribution to journalArticle

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