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Trisections Of Flat Surface Bundles Over Surfaces, Marla Williams

Department of Mathematics: Dissertations, Theses, and Student Research

A trisection of a smooth 4-manifold is a decomposition into three simple pieces with nice intersection properties. Work by Gay and Kirby shows that every smooth, connected, orientable 4-manifold can be trisected. Natural problems in trisection theory are to exhibit trisections of certain classes of 4-manifolds and to determine the minimal trisection genus of a particular 4-manifold.

Let $\Sigma_g$ denote the closed, connected, orientable surface of genus $g$. In this thesis, we show that the direct product $\Sigma_g\times\Sigma_h$ has a $((2g+1)(2h+1)+1;2g+2h)$-trisection, and that these parameters are minimal. We provide a description of the trisection, and an algorithm to generate a …