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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.06178 |
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| _version_ | 1866909685367439360 |
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| author | Bui, Vuong Daneshpajouh, Hamid Reza |
| author_facet | Bui, Vuong Daneshpajouh, Hamid Reza |
| contents | A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two $\mathbb Z/2$-spaces is equal to the minimum of their $\mathbb Z/2$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06178 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A topological version of Hedetniemi's conjecture for equivariant spaces Bui, Vuong Daneshpajouh, Hamid Reza Combinatorics A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two $\mathbb Z/2$-spaces is equal to the minimum of their $\mathbb Z/2$-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. |
| title | A topological version of Hedetniemi's conjecture for equivariant spaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2302.06178 |