Tight contact structures on some small Seifert fibered 3-manifolds

Paolo Ghiggini, Paolo Lisca, András I. Stipsicz

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Abstract

We classify tight contact structures on the small Seifert fibered 3-manifolds M(-1; r1, r2, r3) with r i ∈ (0, 1) ∩ ℚ and r1, r2 ≥ 1/2. The result is obtained by combining convex surface theory with computations of contact Ozsváth-Szabó invariants. We also show that some of the tight contact structures on the manifolds considered are nonfillable, justifying the use of Heegaard Floer theory.

Original languageEnglish
Pages (from-to)1403-1447
Number of pages45
JournalAmerican Journal of Mathematics
Volume129
Issue number5
DOIs
Publication statusPublished - Oct 1 2007

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ASJC Scopus subject areas

  • Mathematics(all)

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