Methods from Differential Geometry in Polytope Theory

2014/03/11 by Adiprasito, Karim Alexander
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1403.2657

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.

Related

• Simplicial Polytope Complexes and Deloopings of K-theory
• Differential algebra of polytopes and inversion formulas
• Problems on Polytopes, Their Groups, and Realizations
• Toric Topology. Chapter 1: Geometry and combinatorics of polytopes
• Notes on Convex Sets, Polytopes, Polyhedra, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations