
## 3. Relative trisections

1. #### Problem 3.1.

Suppose $X$ is a smooth, oriented $4$-manifold with boundary. Consider an open book decomposition on $M=\partial X$ and let $T$ be a relative trisection for $X$ corresponding to this open book. What conditions on $T$ implies that the open book supports a tight contact structure?

Remark: Define a notion of compatibility between trisection and symplectic structure. Find the sufficient conditions on the trisection which implies that it is a geometric filling e.g. symplectic filling with a convex or concave boundary.
• #### Problem 3.2.

For $4$-manifolds with boundary, how trisection genus changes under boundary connected sum?

Cite this as: AimPL: Trisections and low-dimensional topology, available at http://aimpl.org/trisections.