Equivariant Lagrangian displacements

2025/10/23 by Cant, Dylan, Christ, Julio Sampietro
#53D12 53D20 53D45 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2510.20756

Abstract

This paper proves that certain monotone Lagrangians in the standard symplectic vector space cannot be displaced by a Hamiltonian isotopy which commutes with the antipodal map. The method of proof is to develop a Borel equivariant version of the quantum cohomology of Biran and Cornea, and prove it is sensitive to equivariant displacements. The Floer--Euler class of Biran and Khanevsky appears as a term in the equivariant differential in certain cases.

Citations

• Equivariant Floer homology is isomorphic to reduced Floer homology
• Parametric Gromov width of Liouville domains
• Bordism classes of loops and Floer's equation in cotangent bundles
• Adiabatic compactness for holomorphic curves with boundary on nearby Lagrangians
• Floer homology of Lagrangians in clean intersection
• The equivariant pair-of-pants product in fixed point Floer cohomology
• Symplectic cohomology and Viterbo's theorem
• A Floer-Gysin exact sequence for Lagrangian submanifolds
• Localization for involutions in Floer cohomology
• Quantum Structures for Lagrangian Submanifolds
• Holomorphic disc, spin structures and Floer cohomology of the Clifford torus

Related

• Equivariant Lagrangian correspondence and a conjecture of Teleman
• Lagrangian Non-Intersections
• Equivariant Floer homology is isomorphic to reduced Floer homology
• Canonical equivariant extensions using classical Hodge theory
• Equivariant symplectic Hodge theory and the d_Gδ-lemma