{"paper":{"title":"Cancellation for 4-manifolds with virtually abelian fundamental group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Qayum Khan","submitted_at":"2016-06-20T04:22:11Z","abstract_excerpt":"Suppose $X$ and $Y$ are compact connected topological 4-manifolds with fundamental group $\\pi$. For any $r \\geqslant 0$, $Y$ is $r$-stably homeomorphic to $X$ if $Y \\# r(S^2 \\times S^2)$ is homeomorphic to $X \\# r(S^2\\times S^2)$. How close is stable homeomorphism to homeomorphism?\n  When the common fundamental group $\\pi$ is virtually abelian, we show that large $r$ can be diminished to $n+2$, where $\\pi$ has a finite-index subgroup that is free-abelian of rank $n$. In particular, if $\\pi$ is finite then $n=0$, hence $X$ and $Y$ are $2$-stably homeomorphic, which is one $S^2 \\times S^2$ summa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05968","kind":"arxiv","version":1},"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"}