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Contact surgeries and the transverse invariant in knot Floer homology

Part of: Differential topology Low-dimensional topology

Published online by Cambridge University Press:  11 May 2010

Peter Ozsváth  and
András I. Stipsicz
Peter Ozsváth
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA ([email protected])
András I. Stipsicz
Affiliation:
Alfréd Rényi Institute of Mathematics, PO Box 127, H-1364 Budapest, Hungary and Department of Mathematics, Columbia University, New York, NY 10027, USA ([email protected])
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Abstract

We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg–Chekanov twist knots En are not transversely simple for n odd and n > 3.

Keywords

Legendrian knotstransverse knotsHeegaard Floer homology

MSC classification

Secondary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 3 , July 2010 , pp. 601 - 632
Copyright
Copyright © Cambridge University Press 2010

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