We obtain some explicit calculations of crossedQ-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups. Introduction A crossed module M = (μ : M → P ) has a classifying space BM (...

We give combinatorial models for the homotopy type of complements elliptic arrangements (i.e., certain sets abelian subvarieties in a product curves). presentation fundamental group such spaces and, as an application, we treat case ordered configuration curves. Our are finite polyhedral CW complexes, and our tools choice acyclic categories (small without loops). As stepping stone, characterizat...

An affine projection π : P p → Qq of convex polytopes induces an inclusion map of the face posets i : F(Q) → F(P ). We define an order-preserving map of posets h : F(P ) → Suspp−qF(Q) such that for any filter J of Suspp−qF(Q), the map h restricts to a homotopy equivalence between the order complexes of h−1(J) and J . As applications we prove (1) A conjecture of Stanley [11] concerning the relat...