A class of tight contact structures on Σ2 × I

Cofer, Tanya

doi:10.2140/agt.2004.4.961

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

Tanya Cofer

Algebraic & Geometric Topology 4 (2004) 961–1011

DOI: 10.2140/agt.2004.4.961

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/

Volume 4, issue 2 (2004)