论文标题
最佳的彩色tverberg定理用于主要力量
Optimal colored Tverberg theorems for prime powers
论文作者
论文摘要
Blagojević，Matschke和Ziegler的彩色TVERBERG定理为有色Tverberg问题提供了最佳的边界，这是在相交的彩虹简单数量的条件下是质量数字。我们将此结果扩展到最佳的彩色tverberg定理，用于多点的多集，这对于每个质量功率$ r = p^k $有效。主要的新想法之一是，用较小维度的“删节的单纯形”替换原始Tverberg定理中使用的环境简称$Δ^n $，并通过允许在不同的Rainbow简单中反复出现顶点来弥补这种降低。在证明中使用的配置空间是组合伪行的组合，可以表示为多个棋盘络合物。我们的主要拓扑工具是对非自由作用的eilenberg-krasnoselskii理论。
The type A colored Tverberg theorem of Blagojević, Matschke, and Ziegler provides optimal bounds for the colored Tverberg problem, under the condition that the number of intersecting rainbow simplices is a prime number. We extend this result to an optimal, type A colored Tverberg theorem for multisets of colored points, which is valid for each prime power $r=p^k$. One of the principal new ideas is to replace the ambient simplex $Δ^N$, used in the original Tverberg theorem, by an "abridged simplex" of smaller dimension, and to compensate for this reduction by allowing vertices to repeatedly appear a controlled number of times in different rainbow simplices. Configuration spaces, used in the proof, are combinatorial pseudomanifolds which can be represented as multiple chessboard complexes. Our main topological tool is the Eilenberg-Krasnoselskii theory of degrees of equivariant maps for non-free actions.
