# Trisection genus

From Manifold Atlas

## [edit] 1 Problem

Let be a closed smooth -manifold. The *trisection genus* of is the minimal genus of the central surface appearing in a trisection of .

**Question:** Is the trisection genus additive under connected sum?

If so, then the following hold

- The trisection genus of is a homeomorphism invariant.
- The manifolds , , , and have a unique smooth structure.