Heegaard–Floer homology and string links

Roberts, Lawrence

doi:10.2140/agt.2009.9.29

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Heegaard–Floer homology and string links

Lawrence Roberts

Algebraic & Geometric Topology 9 (2009) 29–101

DOI: 10.2140/agt.2009.9.29

Abstract

We extend knot Floer homology to string links in $D^{2} \times I$ 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 $D^{2} \times I$ ) 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

Volume 9, issue 1 (2009)