{"paper":{"title":"Z2-indices and Hedetniemi's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Takahiro Matsushita","submitted_at":"2017-10-15T06:59:55Z","abstract_excerpt":"The $\\mathbb{Z}_2$-index ${\\rm ind}(X)$ of a $\\mathbb{Z}_2$-CW-complex $X$ is the smallest number $n$ such that there is a $\\mathbb{Z}_2$-map from $X$ to $S^n$. Here we consider $S^n$ as a $\\mathbb{Z}_2$-space by the antipodal map. Hedetniemi's conjecture is a long standing conjecture in graph theory concerning the graph coloring problem of tensor products of finite graphs. We show that if Hedetniemi's conjecture is true, then ${\\rm ind}(X \\times Y) = \\min \\{ {\\rm ind}(X) , {\\rm ind}(Y)\\}$ for every pair $X$ and $Y$ of finite $\\mathbb{Z}_2$-complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05290","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}