Georgia Institute of Technology College of Sciences

Trisections of 4-manifolds relative to their boundary were introduced by Gay and Kirby in 2012. They are decompositions of 4-manifolds that induce open book decomposition in the bounding 3-manifolds. This talk will focus on diagrams of relative trisections and will be divided in two. In the first half I will focus on trisections as fillings of open book decompositions and I will present different fillings of different open book decompositions of the Poincare homology sphere. In the second half I will show examples of trisections of pieces of some of the surgery techniques that result in exotic 4-manifolds.