Real link Floer homology

Abstract

In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homology and real sutured Heegaard Floer homology. We give a combinatorial description of the theory in $S^3$ via real grid diagrams and use it to investigate structural properties of the theory as well as properties of strongly invertible knots. A computer implementation was written by Zhenkun Li. An appendix including real grid homology for 50+ small knots is made jointly by Zhenkun Li and the author, from which we observe several interesting phenomenon.