Seifert fibered contact three-manifolds via surgery

Lisca, Paolo; Stipsicz, Andras I

doi:10.2140/agt.2004.4.199

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Seifert fibered contact three-manifolds via surgery

Paolo Lisca and Andras I Stipsicz

Algebraic & Geometric Topology 4 (2004) 199–217

DOI: 10.2140/agt.2004.4.199

arXiv: math.SG/0307341

Abstract

Using contact surgery we define families of contact structures on certain Seifert fibered three–manifolds. We prove that all these contact structures are tight using contact Ozsváth–Szabó invariants. We use these examples to show that, given a natural number $n$ , there exists a Seifert fibered three–manifold carrying at least $n$ pairwise non-isomorphic tight, not fillable contact structures.

Keywords

Seifert fibered 3–manifolds, tight, fillable contact structures, Ozsváth–Szabó invariants

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 57R57

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Publication

Received: 6 October 2003

Accepted: 31 March 2004

Published: 10 April 2004

Authors

Paolo Lisca
Dipartimento di Matematica Università di Pisa I-56127 Pisa Italy

Andras I Stipsicz
Rényi Institute of Mathematics Hungarian Academy of Sciences H-1053 Budapest Reáltanoda utca 13–15 Hungary

Volume 4, issue 1 (2004)