Strong Topological Rigidity of Non-Compact Orientable Surfaces

Sumanta Das

doi:10.2140/agt.2024.24.4423

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arXiv · 2111.11194

Strong Topological Rigidity of Non-Compact Orientable Surfaces

Sumanta Das

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Abstract

We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided surfaces are neither the plane nor the punctured plane. Thus all non-compact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense.

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Sumanta Das. 2021-11-22. Strong Topological Rigidity of Non-Compact Orientable Surfaces. https://doi.org/10.2140/agt.2024.24.4423

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