Authors: Jojić, Duško
Panina, Gaiane
Živaljević, Rade 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A Tverberg type theorem for collectively unavoidable complexes
Journal: Israel Journal of Mathematics
Issue Date: 1-Jan-2021
Rank: ~M22
ISSN: 0021-2172
DOI: 10.1007/s11856-021-2087-3
Abstract: 
We prove that the symmetrized deleted join SymmDelJoin(K) of a “balanced family” K= 〈Ki〉i=1r of collectively r-unavoidable subcomplexes of 2[m] is (m−r−1)-connected. As a consequence we obtain a Tverberg-Van Kampen-Flores type result which is more conceptual and more general than previously known results. Already the case r = 2 of this result seems to be new as an extension of the classical Van Kampen-Flores theorem. The main tool used in the paper is R. Forman’s discrete Morse theory.
Publisher: Springer Link

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