Hello everyone,

This week we are really excited to have Roman Aranda (virtually) coming down from Iowa to speak.

His title and abstract are below:

4-manifolds with small trisection genus
Speaker: 

Abstract: In 2016, D. Gay and R. Kirby proved that every closed 4-manifold can be decomposed as the union of three 4-dimensional simple pieces with triple intersection a closed orientable surface of genus g. This decomposition is called a trisection of genus g for M. In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the rank of its fundamental group. In this talk, we show that given a group G, there exists a 4-manifold M with fundamental group G with trisection genus achieving Chu-Tillmann’s lower bound. The proof uses techniques of knot theory in simple 3-manifolds.

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Neil Hoffman