# Towards thin triangulations of 3-manifolds

## Kristóf Huszár

November 4, 2021, 12:20 in S6

## Abstract

There are several computationally hard problems about triangulated 3-manifolds that admit an efficient algorithmic solution, provided the input triangulation is sufficiently "thin." Exhibiting such triangulations is therefore a compelling task, however, this can be limited by the topology of the underlying manifold.

In this talk I give an overview of recent results that link the key combinatorial parameters in the above context to classical topological invariants of 3-manifolds in a quantitative way. We establish these results through constructions involving generalized Heegaard splittings and layered triangulations of 3-manifolds.

Joint work with Jonathan Spreer and Uli Wagner.