A Topological Version of Hedetniemi’s Conjecture for Equivariant Spaces

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Abstract

A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two Z/ 2 - spaces is equal to the minimum of their Z/ 2 -indexes. The main purpose of this article is to study the topological version of the Hedetniemi conjecture for G-spaces. Indeed, we show that the topological Hedetniemi conjecture cannot be valid for general pairs of G-spaces. More precisely, we show that this conjecture can possibly survive if the group G is either a cyclic p-group or a generalized quaternion group whose size is a power of 2.

Original languageEnglish
JournalCombinatorica
DOIs
Publication statusAccepted/In press - 2023

Keywords

  • Cross-index
  • Hedetniemi’s conjecture
  • Mapping index

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

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