Tight contact structures of certain Seifert fibered 3-manifolds with e₀ = −1

Jinhong Kim

Vol. 221 (2005), No. 1, 109–122

DOI: 10.2140/pjm.2005.221.109

Abstract

We classify, up to contact isotopy, all tight contact structures on a family of Seifert fibered three-manifolds M−,, satisfying 0 < < . We show that, if [r₀,r₁,…,r_l] is the continued fraction expansion of −, there are exactly |r₀+5||r₁+1|⋯|r_l+1| tight contact structures on such Seifert fibered three-manifolds M−,, as above, so all the tight contact structures are holomorphically fillable.

Keywords

tight contact structure, Seifert fibered 3-manifold, truncated Euler number

Mathematical Subject Classification 2000

Primary: 57R57

Milestones

Received: 9 October 2003

Revised: 18 October 2004

Accepted: 5 December 2004

Published: 1 September 2005