Methods from Differential Geometry in Polytope Theory
  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. 
Karim Alexander Adiprasito
math.CO math.AT math.DG math.MG