English

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

R2 v1 2026-06-28T08:16:49.590Z