Complements of 2-tori in closed smooth simply connected 4-manifolds that admit a complete finite volume hyperbolic structure

26.02.2019, **15:15**  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Hemanth Saratchandran (Universität Augsburg)

The study of hyperbolic knot complements has a long history leading to many exciting results in the field of 3-manifold topology. In this talk, I will present a 4-dimensional analogue of this study. Namely, I will consider when a closed smooth simply connected 4-manifold can contain a collection of 2-tori, whose complement can admit a complete finite volume hyperbolic structure. I will start by presenting some necessary conditions, based on a classification theorem of S. Donaldson and M. Freedman, and then move on to outline how one can try to build such complements.