Proper Homotopy Nonrigidity of Open Contractible Manifolds

Donghan Kim

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arXiv · 2607.18093

Proper Homotopy Nonrigidity of Open Contractible Manifolds

Donghan Kim

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Abstract

We study whether proper homotopy equivalence classifies open contractible manifolds arising as interiors of compact contractible manifolds. In dimensions three and four, it does: any two such interiors that are properly homotopy equivalent are homeomorphic. In every even dimension $N\geq 6$ and every odd dimension $N\geq 9$, however, it does not: a single proper homotopy type contains infinitely many pairwise nonhomeomorphic smooth open contractible $N$-manifolds. The cases of dimensions five and seven remain unresolved.

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Donghan Kim. 2026-07-20. Proper Homotopy Nonrigidity of Open Contractible Manifolds. https://arxiv.org/abs/2607.18093

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