Topological Tverberg Theorem

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Topological Tvereberg Theorem says that any continuous function from the $(r-1)(d+1)$-simplex to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces where $r$ is a prime power.



For a simplicial complex $K$ and $r$, let $t(K,r)$ be the maximum number $d$ such that any continuous function from the $K$ to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces.




Is it true that $t(K, r)= d$ for any simplicial complex $K$ which is
homeomorphic with the $(r-1)(d+1)$-simplex ($r$ is a prime power)?




Comment: $t(K, r)geq d$ as any such a $K$ contains a $(r-1)(d+1)$-simplex.




discrete-geometry




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    Topological Tvereberg Theorem says that any continuous function from the $(r-1)(d+1)$-simplex to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces where $r$ is a prime power.



    For a simplicial complex $K$ and $r$, let $t(K,r)$ be the maximum number $d$ such that any continuous function from the $K$ to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces.




    Is it true that $t(K, r)= d$ for any simplicial complex $K$ which is
    homeomorphic with the $(r-1)(d+1)$-simplex ($r$ is a prime power)?




    Comment: $t(K, r)geq d$ as any such a $K$ contains a $(r-1)(d+1)$-simplex.




    discrete-geometry




    share|cite|improve this question























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      up vote
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      down vote

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      Topological Tvereberg Theorem says that any continuous function from the $(r-1)(d+1)$-simplex to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces where $r$ is a prime power.



      For a simplicial complex $K$ and $r$, let $t(K,r)$ be the maximum number $d$ such that any continuous function from the $K$ to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces.




      Is it true that $t(K, r)= d$ for any simplicial complex $K$ which is
      homeomorphic with the $(r-1)(d+1)$-simplex ($r$ is a prime power)?




      Comment: $t(K, r)geq d$ as any such a $K$ contains a $(r-1)(d+1)$-simplex.




      discrete-geometry




      share|cite|improve this question













      Topological Tvereberg Theorem says that any continuous function from the $(r-1)(d+1)$-simplex to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces where $r$ is a prime power.



      For a simplicial complex $K$ and $r$, let $t(K,r)$ be the maximum number $d$ such that any continuous function from the $K$ to the $mathbbR^d$ identifies $r$ points from $r$ pairwise disjoint faces.




      Is it true that $t(K, r)= d$ for any simplicial complex $K$ which is
      homeomorphic with the $(r-1)(d+1)$-simplex ($r$ is a prime power)?




      Comment: $t(K, r)geq d$ as any such a $K$ contains a $(r-1)(d+1)$-simplex.





      discrete-geometry





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








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