Hedetniemi's conjecture from the topological viewpoint
Abstract
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 question about computing the index of some nontrivial products, raised by Marcin Wrochna. Finally, some new topological lower bounds for the chromatic number of the Categorical product of (hyper)graphs are presented.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.04963
 Bibcode:
 2018arXiv180604963D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Topology