Seiberg-Witten Floer homotopy contact invariant
Geometric Topology
2021-07-06 v4 Differential Geometry
Abstract
We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer-Mrowka-Ozv\'ath-Szab\'o. 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.
Keywords
Cite
@article{arxiv.2010.02132,
title = {Seiberg-Witten Floer homotopy contact invariant},
author = {Nobuo Iida and Masaki Taniguchi},
journal= {arXiv preprint arXiv:2010.02132},
year = {2021}
}
Comments
53 pages, Theorem 1.5, 1.6, 1.7, 1.8, 1.9 are deleted, Theorem 1.5 and 1.6 have no new concrete examples, Theorem 1.7-1.9 contain some essential mistakes in the previous version