Optimal bounds for the colored Tverberg problem

Pavle V. M. Blagojević; Benjamin Matschke; Günter M. Ziegler

Journal of the European Mathematical Society (2015)

  • Volume: 017, Issue: 4, page 739-754
  • ISSN: 1435-9855

Abstract

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We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.

How to cite

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Blagojević, Pavle V. M., Matschke, Benjamin, and Ziegler, Günter M.. "Optimal bounds for the colored Tverberg problem." Journal of the European Mathematical Society 017.4 (2015): 739-754. <http://eudml.org/doc/277250>.

@article{Blagojević2015,
abstract = {We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.},
author = {Blagojević, Pavle V. M., Matschke, Benjamin, Ziegler, Günter M.},
journal = {Journal of the European Mathematical Society},
keywords = {optimal colored Tverberg theorem; Bárány–Larman conjecture; equivariant obstruction theory; chessboard complexes; optimal colored Tverberg theorem; Barany-Larman conjecture; equivariant obstruction theory; chessboard complexes},
language = {eng},
number = {4},
pages = {739-754},
publisher = {European Mathematical Society Publishing House},
title = {Optimal bounds for the colored Tverberg problem},
url = {http://eudml.org/doc/277250},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Blagojević, Pavle V. M.
AU - Matschke, Benjamin
AU - Ziegler, Günter M.
TI - Optimal bounds for the colored Tverberg problem
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 4
SP - 739
EP - 754
AB - We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
LA - eng
KW - optimal colored Tverberg theorem; Bárány–Larman conjecture; equivariant obstruction theory; chessboard complexes; optimal colored Tverberg theorem; Barany-Larman conjecture; equivariant obstruction theory; chessboard complexes
UR - http://eudml.org/doc/277250
ER -

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