A trisection of a smooth, connected 4-manifold is a decomposition into three standard pieces. Like the case of Heegaard splittings in dimension three, a trisection is described by a trisection diagram: three sets of curves in a surface satisfying some properties. In general, it is not evident whether two trisection diagrams represent the same decomposition or how the diagram of a given trisection looks like. $\star$-trisections increase the “allowed” diagrams and permit us to address those problems in new families of examples.

In this talk, I will introduce $\star$-trisections: a generalization of trisection. The main goal of the talk is to describe concrete examples of how to use $\star$-trisections to draw trisections for new 4-manifolds. This is joint work with Jesse Moeller.

Host: Tye Lidman

Instructions to join: Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact the host to get the link.