Combinatorial cobordism maps in hat Heegaard Floer theory

Details Combinatorial cobordism maps in hat Heegaard Floer theory Combinatorial cobordism maps in hat Heegaard Floer theory

2006-11-30

arxiv.org/abs/math/0611927v3

Mathematics

Geometric Topology

34 pages, 31 figures; discussion now limited to cobordisms satisfying a homological assumption; Section 4 completely rewritten

Scientific paper

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.

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