Equivariant Floer cohomology for contactomorphisms of quotient spaces

2026/02/24 by Dylan Cant, Eric Kilgore, Jun Zhang · 1 voice · 1 citation
Mathematics · #math.SG

paper · pdf

arxiv published 2026/02/24 · arxiv updated 2026/05/16

Abstract

This paper establishes the orderability of contact manifolds which are quotients of fillable contact manifolds under finite group actions compatible with the filling, the prototypical example being ℝP^2n-1 as the quotient of S^2n-1. Our approach employs an equivariant formulation of the so-called contact Floer cohomology theory. This leads us to develop an analogue of Givental's nonlinear Maslov index using the k[[x]]-module structure on an equivariant version of contact Floer cohomology. A key idea is that mapping cones of continuation maps detect crossings with the discriminant (recall that Givental's index is a continuous integer valued function on the complement of the discriminant). To properly handle the inherent non-canonicity in defining such mapping cones, we lift the structure of contact Floer cohomology to chain level by defining it as an ∞-functor on a suitable ∞-categorification of the Eliashberg-Polterovich orderability relation on the universal cover of the contactomorphism group.

Cited by

• The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in ℝ⁴

Discussions

• Dylan Cant, Eric Kilgore, Jun Zhang: Equivariant Floer cohomology for contactomorphisms of quotient spaces https://arxiv.org/abs/2602.21152 https://arxiv.org/pdf/2602.21152 https://arxiv.org/html/2602 [bsky, 0 points, 0 comments]

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