Methods from Differential Geometry in Polytope Theory

TL;DR

This thesis explores classical combinatorial objects like polytopes and complexes using advanced tools from differential geometry, topology, and geometric group theory to gain new insights and methods.

Contribution

It introduces novel applications of differential geometric tools to the study of polytopes, bridging combinatorics with topology and geometry.

Findings

New geometric methods for analyzing polytopes

Connections established between combinatorial topology and differential geometry

Enhanced understanding of subspace arrangements

Abstract

The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-dimensional topology.