We prove combinatorial formulas for the homotopy type of the union of the subspaces in an (affine, compactified affine, spherical or projective) subspace arrangement. From these formulas we derive… Expand

Abstract We provide a “toolkit” of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used in quite… Expand

Abstract An old problem in combinatorial geometry is to determine when one or more measurable sets in R d admit an equipartition by a collection of k hyperplanes [B. Grunbaum, Partitions of… Expand

Sierksma's conjecture is that, for every general position linear maph: Δ(q−1)(d+1) →Rd, there exist at leastv different collections {Δt1, ..., Δtq} of disjoint faces of Δ(Q−1) with the property thatf(ΔT1) ∩ ... ∩f( Δtq) ≠ Ø.Expand