Abstract
There are various ways one might define a notion of “width” for 3-dimensional manifolds. Well-known examples include the Heegaard genus, the rank of the fundamental group, or, in case of hyperbolic 3-manifolds, the volume.
Motivated by the algorithmic study of 3-manifolds, recently there has been a growing interest in the study of combinatorial width parameters defined through triangulations: It has been shown that several computationally hard problems can be efficiently solved for input triangulations that are sufficiently “thin” in a certain sense.
In this talk we give an overview of recent results that link these combinatorial width parameters with classical invariants in a quantitative way. To establish our theorems, we rely on generalized Heegaard splittings and on layered triangulations.
Joint work with Jonathan Spreer and Uli Wagner.
