A Tverberg type theorem for collectively unavoidable complexes

Autor:	Duško Jojić, Gaiane Panina, Rade T. Živaljević
Rok vydání:	2021
Předmět:	Combinatorics 010201 computation theory & mathematics General Mathematics 010102 general mathematics Discrete Morse theory 0102 computer and information sciences Join (topology) Extension (predicate logic) 0101 mathematics Algebra over a field Type (model theory) 01 natural sciences Mathematics
Zdroj:	Israel Journal of Mathematics. 241:17-36
ISSN:	1565-8511 0021-2172
DOI:	10.1007/s11856-021-2087-3
Popis:	We prove that the symmetrized deleted join SymmDelJoin( $$\mathcal{K}$$ ) of a “balanced family” $$\mathcal{K}$$ = 〈Ki〉 =1 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::958296165d7a02f5e48d184484e9b283 https://doi.org/10.1007/s11856-021-2087-3 Zobrazit plný text záznamu Full text from SpringerLink