The Weinstein Conjecture for Planar Contact Structures in Dimension Three

Abstract

In this paper we describe a general strategy for approaching the Weinstein conjecture in dimension three. We apply this approach to prove the Weinstein conjecture for a new class of contact manifolds (planar contact manifolds). We also discuss how the present approach reduces the general Weinstein conjecture in dimension three to a compactness problem for the solution set of a first order elliptic PDE.

19 pages, corrected some typos

References in corpus (1)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures

Cited by in corpus (5)

• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• Planar open books and Floer homology
• Strong fillability and the Weinstein conjecture
• Explicit horizontal open books on some Seifert fibered 3--manifolds
• Explicit horizontal open books on some plumbings