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Lectures on Contact Geometry in Low-Dimensional Topology

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arxiv math/0610798 v1 pith:2ZNS3Q46 submitted 2006-10-26 math.GT math.SG

classification math.GTmath.SG
keywords contactgeometrydiscusslow-dimensionalsymplectictopologyeliashbergapplication
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This article sketches various ideas in contact geometry that have become useful in low-dimensional topology. Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact structures, (2) discuss Eliashberg and Weinstein's symplectic handle attachments, and (3) briefly discuss Giroux's insights into open book decompositions and contact geometry. Bringing these pieces together we discuss the construction of ``symplectic caps'' which are a key tool in the application of contact/symplectic geometry to low-dimensional topology.

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Cited by 1 Pith paper

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  1. Boundary framings for locally conformally symplectic four-manifolds

    math.AT 2025-02 reject novelty 5.0 of 10

    The paper proposes a rational homotopy model for a classifying space of locally conformally symplectic four-manifolds and a cobordism category of three-manifolds with Omega^2 S^2-bundle framings, but the standalone te...

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