College of Liberal Arts & Sciences

# Topology Seminar

**Abstract: **

A trisection of a smooth connected 4-manifold is a decomposition into three standard pieces. Similar to 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 even what 4-manifold they depict.

In this talk I will explain how to soften the definition of a trisection to answer two questions of Jeff Meier about genus three trisections: (1) The trisections obtained by spinning genus two Heegaard splittings for $L(p,q)$ and $L(p,q')$ are isotopic. (2) The 4-manifolds obtained from the Farey trisection diagrams are all standard. This is joint work with Jesse Moeller.