Abstract:
In the first part of the talk, we will delve into surface bundles over the circle. Specifically, we will discuss open book decompositions of closed three-dimensional manifolds, the primary examples of which arise in the context of fibered knots and links. This will allow us to extend the bridge from the theory of surface mapping class groups to three-dimensional topology.
In the second part of the talk, we will turn to the concept of plane field distributions on three-dimensional manifolds. In particular, we will examine in detail the construction of three models of the standard contact structure on the three-dimensional sphere. Finally, following Thurston and Winkelnkemper, we will associate a contact structure with each open book.
