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A class of tight contact structures on $\Sigma_2 \times I$

Tanya Cofer

Algebraic & Geometric Topology 4 (2004) 961–1011

arXiv: math.SG/0411208

Abstract

We employ cut and paste contact topological techniques to classify some tight contact structures on the closed, oriented genus–2 surface times the interval. A boundary condition is specified so that the Euler class of the of the contact structure vanishes when evaluated on each boundary component. We prove that there exists a unique, non-product tight contact structure in this case.

Keywords
tight, contact structure, genus-2 surface
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 53C15
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Publication
Received: 9 November 2003
Revised: 20 May 2004
Accepted: 11 June 2004
Published: 31 October 2004
Authors
Tanya Cofer
Department of Mathematics
Northeastern Illinois University
5500 North St Louis Avenue
Chicago IL 60625-4699
USA
http://www.neiu.edu/~tcofer/