Composition Maps in Heegaard Floer Homology
Geometric Topology
2023-06-05 v2
Abstract
We use results of Auroux arXiv:1001.4323 and Zemke arXiv:1801.09270 to prove that, in the morphism spaces formulation of Heegaard Floer homology given in arXiv:1005.1248, the opposite composition map agrees up to homotopy with the map on Heegaard Floer complexes induced by a pair-of-pants cobordism. As an application, we give an algorithm for computing arbitrary cobordism maps on hat Heegaard Floer homology.
Keywords
Cite
@article{arxiv.2301.08882,
title = {Composition Maps in Heegaard Floer Homology},
author = {Jesse Cohen},
journal= {arXiv preprint arXiv:2301.08882},
year = {2023}
}
Comments
v2. 36 pages, adds new section detailing an algorithm for computing arbitrary cobordism maps on hat Heegaard Floer homology