Tverberg plus constraints
Abstract
Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem: For this we introduce a proof technique that combines a concept of "Tverberg unavoidable subcomplexes" with the observation that Tverberg points that equalize the distance from such a subcomplex can be obtained from maps to an extended target space. Thus we obtain simple proofs for many variants of the topological Tverberg theorem, such as the colored Tverberg theorem of Zivaljevic and Vrecica (1992). We also get a new strengthened version of the generalized van KampenFlores theorem by Sarkaria (1991) and Volovikov (1996), an affine version of their "jwise disjoint" Tverberg theorem, and a topological version of Soberon's (2013) result on Tverberg points with equal barycentric coordinates.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 DOI:
 10.48550/arXiv.1401.0690
 arXiv:
 arXiv:1401.0690
 Bibcode:
 2014arXiv1401.0690B
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Topology;
 52A35;
 55S35
 EPrint:
 15 pages