Trisection genus

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1 Problem

Let M be a closed smooth 4-manifold. The trisection genus of M is the minimal genus of the central surface appearing in a trisection of M.

Question: Is the trisection genus additive under connected sum?

If so, then the following hold

  1. The trisection genus of M is a homeomorphism invariant.
  2. The manifolds S^4, \C P^2, S^2 \times S^2, \C P^2 \sharp \C P^2 and \C P^2 \sharp \overline{\C P^2} have a unique smooth structure.

2 References

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