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2009 Heegaard–Floer homology and string links
Lawrence Roberts
Algebr. Geom. Topol. 9(1): 29-101 (2009). DOI: 10.2140/agt.2009.9.29

Abstract

We extend knot Floer homology to string links in D2×I and to d–based links in arbitrary three manifolds. As with knot Floer homology we obtain a description of the Euler characteristic of the resulting homology groups (in D2×I) in terms of the torsion of the string link. Additionally, a state summation approach is described using the equivalent of Kauffman states. Furthermore, we examine the situation for braids, prove that for alternating string links the Euler characteristic determines the homology, and develop similar composition formulas and long exact sequences as in knot Floer homology.

Citation

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Lawrence Roberts. "Heegaard–Floer homology and string links." Algebr. Geom. Topol. 9 (1) 29 - 101, 2009. https://doi.org/10.2140/agt.2009.9.29

Information

Received: 17 January 2007; Revised: 18 June 2008; Accepted: 9 November 2008; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1168.57012
MathSciNet: MR2471131
Digital Object Identifier: 10.2140/agt.2009.9.29

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright © 2009 Mathematical Sciences Publishers

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