Knots which admit a surgery with simple knot Floer homology groups

Eftekhary, Eaman

doi:10.2140/agt.2011.11.1243

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Knots which admit a surgery with simple knot Floer homology groups

Eaman Eftekhary

Algebraic & Geometric Topology 11 (2011) 1243–1256

DOI: 10.2140/agt.2011.11.1243

Abstract

We show that if a positive integral surgery on a knot $K$ inside a homology sphere $X$ results in an induced knot $K_{n} \subset X_{n} (K) = Y$ which has simple Floer homology then $n \geq 2 g (K)$ . Moreover, for $X = S^{3}$ the three-manifold $Y$ is an $L$ –space, and the Heegaard Floer homology groups of $K$ are determined by its Alexander polynomial.

Keywords

simple knot Floer homology, L–space surgery

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57R58

References

Publication

Received: 19 March 2010

Revised: 31 August 2010

Accepted: 11 December 2010

Published: 4 May 2011

Authors

Eaman Eftekhary
School of Mathematics Institute for Research in Fundamental Sciences (IPM) PO Box 19395-5746 Tehran 19395 Iran

Volume 11, issue 3 (2011)