# Trisection genus

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## Revision as of 08:45, 31 August 2020

## 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.