Fillings of Contact 3 Manifolds and Relations in Mapping Class Groups of Surfaces

Geometry Topology Student Seminar
Wednesday, February 5, 2020 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Agniva Roy – Georgia Tech
Hongyi Zhou

A useful way of studying contact 3 manifolds is by looking at their open book decompositions. A result of Akbulut-Ozbagci, Ghiggini, and Loi-Piergallini showed that the manifold is filled by a Stein manifold if and only if the monodromy of an open book can be factorised as the product of positive Dehn twists. Then, the problem of classifying minimal fillings of contact 3 manifolds, or answering questions about which manifolds can be realised by Legendrian surgery, becomes questions about finding factorisations for a given mapping class. This talk will be expository and expand upon how these mapping classes come up, and also discuss known results, techniques, and future directions for research.