Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Inspired by Hempel’s useful complexity for Heegaard splittings, Kirby and Thompson defined an invariant of a smooth 4-manifold using a certain complex of curves on trisection surfaces. The invariant was also generalized to the settings of manifolds with boundaries and surface-links in the 4-sphere by Castro et al. and Blair et al.In this talk, I will discuss a version of the invariant for more general multi-sected knotted surfaces such as complex curves in the complex projective plane. We will see that if the complexity is low, then the (surface, manifold)-pair has simple topology analogous to the results in the previous settings. This is based on work conducted at the University of Central Florida supported by Maggy Tomova.