math_groups_discgeom

A tight colored Tverberg theorem for maps to manifolds (extended abstract)

Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler— 2011

Focus Area 3: Topological connectivity and diameter of Discrete Structures Any continuous map of an N-dimensional simplex ΔN with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of ΔN to the same point in M, assuming that N≥(r-1)(d+1), no r vertices of ΔN get the same color, and our proof needs that r is a prime. A face of ΔN is called a rainbow face if all vertices have different colors. This result is an extension of our recent ``new colored Tverberg theorem'', the special case of M=ℝd. It is also a generalization of Volovikov's 1996 topological Tverberg theorem for maps to manifolds, which arises when all color classes have size 1 (i.e., without color constraints); for this special case Volovikov's proofs, as well as ours, work when r is a prime power.

TitleA tight colored Tverberg theorem for maps to manifolds (extended abstract)
AuthorPavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
Date2011
Source(s)
Appeared InIn Proc. FPSAC 2011 (Reykjavík, Iceland), Discrete Mathematics and Theoretical Computer Science (DMTCS), Vol. AO, http://www.dmtcs.org, page 183–190, 2011.
TypeText