Nonseparating spheres and twisted Heegaard Floer homology

Ni, Yi

doi:10.2140/agt.2013.13.1143

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Nonseparating spheres and twisted Heegaard Floer homology

Yi Ni

Algebraic & Geometric Topology 13 (2013) 1143–1159

DOI: 10.2140/agt.2013.13.1143

Abstract

If a $3$ –manifold $Y$ contains a nonseparating sphere, then some twisted Heegaard Floer homology of $Y$ is zero. This simple fact allows us to prove several results about Dehn surgery on knots in such manifolds. Similar results have been proved for knots in $L$ –spaces.

Keywords

twisted Heegaard Floer homology, nonseparating sphere, Thurston norm, fibered knot, cosmetic surgery

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57R58

References

Publication

Received: 1 September 2010

Accepted: 10 December 2012

Published: 17 April 2013

Authors

Yi Ni
Department of Mathematics, 253-37 California Institute of Technology 251 Sloan Hall 1200 E California Blvd Pasadena, CA 91125 USA
http://www.its.caltech.edu/~yini/

Volume 13, issue 2 (2013)