Author： Ding Fan Geiges Hansjrg van Koert Otto
Publisher： Oxford University Press
ISSN： 0024-6107
Source： Journal of the London Mathematical Society, Vol.86, Iss.3, 2012-12, pp. : 657-682
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Abstract
According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle moves on such diagrams that do not change the corresponding contact manifold. As an application, we derive classification results for subcritically Stein fillable contact 5-manifolds and characterize the standard contact structure on the 5-sphere in terms of such fillings. This characterization is discussed in the context of the AndrewsCurtis conjecture concerning presentations of the trivial group. We further illustrate the use of such diagrams by a covering theorem for simply connected spin 5-manifolds and a new existence proof for contact structures on simply connected 5-manifolds.
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