
## 4. Group trisections

1. #### Problem 4.1.

Use the theory of group trisections to find invariants of $4$-manifold trisections.
• #### Problem 4.2.

Define a notion of group trisection for trisections with boundary.
• #### Problem 4.3.

Adapt group trisections to the setting of bridge trisections and use it to get invariants of knotted surfaces in $S^4$.
• #### Problem 4.4.

Accourding to a classical theorem by Wall, any two homotopoy equivalent, simply connected smooth closed $4$-manifolds $X$ and $Y$ become diffeomorphic after stabilizing by taking connected sums with some number of $S^1\times S^2$’s. What does it says about trisections of the trivial group?

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