## Duke Mathematical Journal

### Combinatorial cobordism maps in hat Heegaard Floer theory

#### Abstract

In a previous article, Sarkar and Wang [15] 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

#### Article information

Source
Duke Math. J., Volume 145, Number 2 (2008), 207-247.

Dates
First available in Project Euclid: 20 October 2008

https://projecteuclid.org/euclid.dmj/1224508836

Digital Object Identifier
doi:10.1215/00127094-2008-050

Mathematical Reviews number (MathSciNet)
MR2449946

Zentralblatt MATH identifier
1153.57027

Subjects
Primary: 57R58: Floer homology
Secondary: 57R56: Topological quantum field theories

#### Citation

Lipshitz, Robert; Manolescu, Ciprian; Wang, Jiajun. Combinatorial cobordism maps in hat Heegaard Floer theory. Duke Math. J. 145 (2008), no. 2, 207--247. doi:10.1215/00127094-2008-050. https://projecteuclid.org/euclid.dmj/1224508836

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