2.00 pm - 3:00 pm, Seminar Hall
MSc RESEARCH SEMINAR TALK
Existence of contact structures on 3-manifold
Yash Deshmukh
Chennai Mathematical Institute.
22-11-17

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Abstract

Starting with definition and basic examples of contact structure we obtain an explicit description of neighborhood of a transverse knot. Using this and the Dehn surgery description of a closed oriented 3-manifold we show that any such manifold supports a contact structure. Further, we describe the 'Lutz twist' and use it to prove that any even class in the second (integral) cohomology group of such a manifold can be realized as the euler class of a contact structure. If time permits we prove, in the special case of $S^3$, the statement that any co-oriented 2-plane field on a closed, orientable 3-manifold can in fact be homotoped to a contact structure.