• Publications
  • Influence
Topological Methods
  • R. Zivaljevic
  • Mathematics, Computer Science
  • Handbook of Discrete and Computational Geometry…
  • 2004
  • 211
  • 17
Homotopy types of subspace arrangements via diagrams of spaces
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 deriveExpand
  • 122
  • 16
  • PDF
The Colored Tverberg's Problem and Complexes of Injective Functions
TLDR
We estimate that the number of halving hyperplanes for a set of n points in Rd satisfies the inequality hd(n)< O(nd−e) for some e > 0. Expand
  • 155
  • 7
  • PDF
Homotopy colimits – comparison lemmas for combinatorial applications
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 quiteExpand
  • 97
  • 6
  • PDF
Topology and combinatorics of partitions of masses by hyperplanes
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 ofExpand
  • 35
  • 6
  • PDF
An Extension of the Ham Sandwich Theorem
  • 61
  • 4
Note on a conjecture of sierksma
TLDR
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
  • 39
  • 4
Chessboard complexes indomitable
TLDR
We give a simpler, degree-theoretic proof of the striking new Tverberg type theorem of Blagojevic, Ziegler and Matschke. Expand
  • 27
  • 4
  • PDF