#### Volume 13, issue 2 (2013)

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Nonseparating spheres and twisted Heegaard Floer homology

### Yi Ni

Algebraic & Geometric Topology 13 (2013) 1143–1159
##### 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
Primary: 57M27
Secondary: 57R58
##### 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/