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

0. Introduction A number of questions from a variety of areas of mathematics lead one to the
problem of analyzing the topology of as implicial complex. We will see some examples in …

Hom (G, H) is a polyhedral complex defined for any two undirected graphs G and H. This
construction was introduced by Lovász to give lower bounds for chromatic numbers of …

We extend the combinatorial Morse complex construction to arbitrary free chain complexes,
and give a short, self-contained, and elementary proof of the quasi-isomorphism between …

Combinatorics, in particular graph theory, has a rich history of being a domain of successful
applications of tools from other areas of mathematics, including topological methods. Here …

In 1998, Forman introduced discrete Morse theory as a tool for studying CW complexes by
producing smaller, simpler-to-understand complexes of critical cells with the same homotopy …

The chromatic alpha filtration is a generalization of the alpha filtration that can encode
spatial relationships among classes of labelled point cloud data, and has applications in …

In a seminal 1994 paper Lusztig (1994)[26], Lusztig extended the theory of total positivity by
introducing the totally non-negative part (G/P)⩾ 0 of an arbitrary (generalized, partial) flag …

We study the restrictions, the strict fixed points, and the strict quotients of the partition
complex| Π n| |n|, which is the Σ n n-space attached to the poset of proper nontrivial …

In this paper we study quotients of posets by group actions. In order to define the quotient
correctly we enlarge the considered class of categories from posets to loopfree categories …