Computing knot Floer homology in cyclic branched covers

Levine, Adam Simon

doi:10.2140/agt.2008.8.1163

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Computing knot Floer homology in cyclic branched covers

Adam Simon Levine

Algebraic & Geometric Topology 8 (2008) 1163–1190

DOI: 10.2140/agt.2008.8.1163

Abstract

We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot $K \subset S^{3}$ in its $m$ –fold cyclic branched cover $Σ_{m} (K)$ , and we give computations when $m = 2$ for over fifty three-bridge knots with up to eleven crossings.

Keywords

Knot Floer homology, Branched cover

Mathematical Subject Classification 2000

Primary: 57R58

Secondary: 57M12, 57M27

References

Publication

Received: 9 December 2007

Revised: 4 March 2008

Accepted: 5 March 2008

Published: 25 July 2008

Authors

Adam Simon Levine
Department of Mathematics Columbia University 2990 Broadway New York NY 10027 USA

Volume 8, issue 2 (2008)