Combinatorial cobordism maps in hat Heegaard Floer theory
Geometric Topology
2021-11-09 v3 Symplectic Geometry
Abstract
In a previous paper, Sarkar and the third author gave a combinatorial description of the hat version of Heegaard Floer homology for three-manifolds. Given a cobordism between two connected three-manifolds, there is an induced map between their Heegaard Floer homologies. Assume that the first homology group of each boundary component surjects onto the first homology group of the cobordism (modulo torsion). Under this assumption, we present a procedure for finding the rank of the induced Heegaard Floer map combinatorially, in the hat version.
Keywords
Cite
@article{arxiv.math/0611927,
title = {Combinatorial cobordism maps in hat Heegaard Floer theory},
author = {Robert Lipshitz and Ciprian Manolescu and Jiajun Wang},
journal= {arXiv preprint arXiv:math/0611927},
year = {2021}
}
Comments
34 pages, 31 figures; discussion now limited to cobordisms satisfying a homological assumption; Section 4 completely rewritten; various other revisions; this version to appear in Duke Math. J