Opening books as a contact sport

Vitalijs Brejevs

Friday 11th October 14:00-15:00 Maths 311B

Abstract

A fruitful way of studying 3-dimensional manifolds is by representing them as unions of 2-dimensional surfaces. One such representation is called an open book decomposition because it requires a binding (a knot) and pages (surfaces that are bounded by the knot). It turns out, by a theorem of Giroux, that open books on a 3-manifold correspond to contact structures, which can be thought about as a collection of twisting planes on the manifold. I will give a brief overview of these topics by showing you pictures and ignoring technicalities.

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