Lectures on Contact Geometry in Low-Dimensional Topology

Details Lectures on Contact Geometry in Low-Dimensional Topology Lectures on Contact Geometry in Low-Dimensional Topology

2006-10-26

arxiv.org/abs/math/0610798v1

Mathematics

Geometric Topology

33 pages, 15 figures

Scientific paper

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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