论文标题
拓扑结构问题超出了主要力量
The topological Tverberg problem beyond prime powers
论文作者
论文摘要
Tverberg-type理论旨在为简单的复杂$σ$建立足够的条件，以使每个连续的地图$ f \colonσ\ to \ mathbb {r}^d $ maps $ q $ q $ q $ q $ q $ q $从成对的分离脸到$ \ mathbb {r}^d $ in pairwise Dissine froces to in Pairwise Dissine froce这些结果对于$ Q $ a Pripe的功率很丰富。但是，对于至少有两个截然不同的主要除数的$ q $，除了质量电力案例的直接推论外，还不存在保证存在$ q $倍的巧合点的结果。在这里，我们提出了一种一般方法，该方法产生了超出主要力量情况的结果。特别是，我们证明了所有$ Q $的拓扑特贝格问题先前猜想的上限。
Tverberg-type theory aims to establish sufficient conditions for a simplicial complex $Σ$ such that every continuous map $f\colon Σ\to \mathbb{R}^d$ maps $q$ points from pairwise disjoint faces to the same point in $\mathbb{R}^d$. Such results are plentiful for $q$ a power of a prime. However, for $q$ with at least two distinct prime divisors, results that guarantee the existence of $q$-fold points of coincidence are non-existent -- aside from immediate corollaries of the prime power case. Here we present a general method that yields such results beyond the case of prime powers. In particular, we prove previously conjectured upper bounds for the topological Tverberg problem for all $q$.
