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

This paper shows how to construct a discrete Morse function with a relatively small number
of critical cells for the order complex of any finite poset with $\hat {0} $ and $\hat {1} $ from …

Starting categorically, we give simple and precise models for classifying spaces of
equivariant principal bundles. We need these models for work in progress in equivariant …

A quotient of a poset P is a partial order obtained on the equivalence classes of an
equivalence relation  on P;  is then called a congruence if it satisfies certain conditions …

We initiate the study of group actions on (possibly infinite) semimatroids and geometric
semilattices. To every such action is naturally associated an orbit-counting function, a two …

We describe a combinatorial model for the complement of a complexified toric arrangement
by using nerves of acyclic categories. This generalizes recent work of Moci and Settepanella …

The Hom complex of homomorphisms between two graphs was originally introduced to
provide topological lower bounds on the chromatic number. In this paper we introduce new …

We introduce a notion of lexicographic shellability for pure, balanced boolean cell
complexes, modelled after the CL-shellability criterion of Björner and Wachs (Adv. in Math …

Let $ G $ be a discrete group. We prove that the category of $ G $-posets admits a model
structure that is Quillen equivalent to the standard model structure on $ G $-spaces. As is …

We introduce the notion of cone complexes to conveniently handle the quotients of simplicial
complexes by group actions. Cone complexes are a generalization of simplicial complexes …