A Tverberg type theorem for collectively unavoidable complexes

We prove that the symmetrized deleted join SymmDelJoin( $$\mathcal{K}$$ ) of a “balanced family” = ?Ki? =1 collectively r-unavoidable subcomplexes 2[m] is (m?r?1)-connected. As consequence we obtain Tverberg-Van Kampen-Flores type result which more conceptual and general than previously known results. Already case r 2 this seems to be new as an extension classical Van theorem. The main tool used in paper R. Forman’s discrete Morse theory.