Fillings of unit cotangent bundles

Abstract

We study the topology of exact and Stein fillings of the canonical contact structure on the unit cotangent bundle of a closed surface ${\Sigma }_g$, where $g$ is at least 2. In particular, we prove a uniqueness theorem asserting that any Stein filling must be s-cobordant rel boundary to the disk cotangent bundle of ${\Sigma }_g$. For exact fillings, we show that the rational homology agrees with that of the disk cotangent bundle, and that the integral homology takes on finitely many possible values: for example, if $g-1$ is square-free, then any exact filling has the same integral homology and intersection form as $D{T}^{\ast }{\Sigma }_g$.

14 pages; v2: updated introduction

Cited by in corpus (4)

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• Diffeomorphism type of symplectic fillings of unit cotangent bundles
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• Symplectic fillings of unit cotangent bundles of hyperbolic surfaces