Volume 9, issue 1 (2009)

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Heegaard–Floer homology and string links

Lawrence Roberts

Algebraic & Geometric Topology 9 (2009) 29–101
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.

Keywords
String links, Heegaard–Floer homology, knot Floer homology
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25
References
Publication
Received: 17 January 2007
Revised: 18 June 2008
Accepted: 9 November 2008
Published: 6 January 2009
Authors
Lawrence Roberts
Department of Mathematics
Michigan State University
East Lansing
Michigan 48824
USA
http://www.math.msu.edu/~lawrence