Abstract:
In 2016, D. Gay and R. Kirby proved that $M$ can be decomposed as the union of three 4-dimensional 1-handlebodies with pairwise intersection 3-dimensional handlebodies and triple intersection a closed orientable surface of genus $g$. Such decomposition is called a trisection of genus $g$ of $M$. In 2018, M. Chu and S. Tillmann used this to give a lower bound for the trisection genus of a closed 4-manifold in terms of the Euler characteristic of $M$ and the rank of its fundamental group.
     In this talk, we show that given a group $G$, there exist a 4-manifold $M$ with fundamental group $G$ with trisection genus achieving Chu-Tillmann's lower bound.