Composition Maps in Heegaard Floer Homology

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.

arXiv commentv2. 36 pages, adds new section detailing an algorithm for computing arbitrary cobordism maps on hat Heegaard Floer homology