2-Dimension from the topological viewpoint

Hedetniemi's conjecture from the topological viewpoint

This paper is devoted to studying a topological version of the famous Hedetniemi conjecture which says: The $\mathbb Z/2$-index of the Cartesian product of two $\mathbb Z/2$-spaces is equal to the minimum of their $\mathbb Z/2$-indexes. We fully confirm the version of this conjecture for the homological index via establishing a stronger formula for the homological index of the join of $\mathbb Z/2$-spaces. Moreover, we confirm the original conjecture for the case when one of the factors is an $n$-sphere. Analogous results for $\mathbb Z/p$-spaces are presented as well. In addition, we answer a…

通过相交看待曲线的拓扑视角

A topological viewpoint on curves via intersection

本文研究闭曲线能否由相交次数确定，构造并分析 $k$-等价曲线，揭示其与简单曲线相交的性质，并以定量方法联系 Otal 定理。

Dold's Theorem from Viewpoint of Strong Compatibility Graphs

Let $G$ be a non-trivial finite group. The well-known Dold's theorem states that: There is no continuous $G$-equivariant map from an $n$-connected simplicial $G$-complex to a free simplicial $G$-complex of dimension at most $n$. In this paper, we give a new generalization of Dold's theorem, by replacing "dimension at most $n$" with a sharper combinatorial parameter. Indeed, this parameter is the chromatic number of a new family of graphs, called strong compatibility graphs, associated to the target space. Moreover, in a series of examples, we will see that one can hope to infer much more infor…