Seiberg-Witten Floer homotopy contact invariant

2020/10/05 by Iida, Nobuo, Taniguchi, Masaki
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2010.02132

Abstract

We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer-Mrowka-Ozváth-Szabó. Moreover, we prove a gluing formula relating our invariant with the first author's Bauer-Furuta type invariant, which refines Kronheimer-Mrowka's invariant for 4-manifolds with contact boundary. As an application, we give a constraint for a certain class of symplectic fillings using equivariant KO-cohomology.

Related

• The contact invariant in sutured Floer homology
• Filtering the Heegaard Floer contact invariant
• Heegaard Floer homologies and contact structures
• Floer theoretic invariants for 3- and 4-manifolds
• Embedded contact homology and Seiberg-Witten Floer cohomology I