Hostname: page-component-6bf8c574d5-956mj Total loading time: 0 Render date: 2025-02-24T06:29:05.263Z Has data issue: false hasContentIssue false
  • English
  • Français

Explicit concave fillings of contact three-manifolds

Published online by Cambridge University Press:  06 November 2002

DAVID T. GAY
DAVID T. GAY
Affiliation:
Mathematics Department, University of Arizona, 617 N. Santa Rita, P.O. Box 210089, Tucson AZ 85721, U.S.A. e-mail: dtgay@math.arizona.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose that (X,ω) is a symplectic manifold and that there exists a Liouville vector field V defined in a neighbourhood of and transverse to M = ∂X. Then V induces a contact form α = ιVω[mid ]M on M which determines the germ of ω along M. One should think of the contact manifold (M,ξ = ker α) as controlling the behaviour of ω ‘at infinity’. If V points out of X along M then we call (X,ω) a convex filling of (M,ξ), and if V points into X along M then we call (X,ω) a concave filling of (M,ξ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 3 , November 2002 , pp. 431 - 441
Copyright
© 2002 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)