Real link Floer homology
arXiv:2604.21240
Abstract
In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real -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 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 computing real grid homology of knots was written by Zhenkun Li. An appendix including real grid homology of 50+ small knots is made jointly by Zhenkun Li and the author, from which we observe several interesting phenomenon.
76 pages in total= main part of 58 pages, 27 figures plus appendix jointly made with Zhenkun Li of 17 pages. Compare to v2: Remark 1.10 is newly added and original Conjecture 1.12 now becomes Proposition 1.13 and minor changes throughout. Comments are welcome!