### Trisecting Smooth 4-manifolds with Boundary

- Series
- Geometry Topology Seminar
- Time
- Monday, November 16, 2015 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Nick Castro – University of Georgia

A trisection of a smooth, oriented, compact 4-manifold X is a decomposition into three diffeomorphic 4-dimensional 1-handlebodies with certain nice intersections properties. This is a very natural 4-dimensional analog of Heegaard splittings of 3-manifolds. In this talk I will define trisections of closed 4-manifolds, but will quickly move to the case of 4-manifolds with connected boundary. I will discuss how these "relative trisections" interact with open book decompositions on the bounding 3-manifold. Finally, I will discuss a gluing theorem which allows us to glue together relative trisections to induce a trisection on a closed 4-manifold.