Polynomially many genus g surfaces in a hyperbolic 3-manifold

Speaker: Anastasiia Tsvietkova, Assistant Professor
Affiliation: Rutgers University

Abstract

For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. In particular, it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss the universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. This is joint work with Marc Lackenby.