Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of
algebraic topology and discrete mathematics. This volume is the first comprehensive …

Here, the study of torus actions on topological spaces is presented as a bridge connecting
combinatorial and convex geometry with commutative and homological algebra, algebraic …

These lecture notes for the IAS/Park City Graduate Summer School in Geometric
Combinatorics (July 2004) provide an overview of poset topology. These notes include …

This chapter reviews the various fundamental unstable and stable splitting theorems for the
polyhedral product. It presents results on the cohomology of polyhedral products. The …

Given a metric space X and a distance threshold r> 0, the Vietoris–Rips simplicial complex
has as its simplices the finite subsets of X of diameter less than r. A theorem of Jean-Claude …

The nerve theorem is a basic result of algebraic topology that plays a central role in
computational and applied aspects of the subject. In topological data analysis, one often …

This article gives a natural decomposition of the suspension of generalized moment-angle
complexes or partial product spaces which arise as polyhedral product functors described …

Fascinating links between the semantics of concurrent programs and algebraic topology
have been discovered and developed since the 1990s, motivated by the hope that each field …

We develop an analog of Forman's discrete Morse theory for cell complexes in the setting of
cellular resolutions of multigraded monomial modules. In particular, using discrete Morse …

For X a metric space and r> 0 a scale parameter, the Vietoris–Rips simplicial complex
VR<(X; r)(resp. VR≤(X; r)) has X as its vertex set, and a finite subset σ⊆ X as a simplex …