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Strong topological rigidity of noncompact orientable surfaces

Sumanta Das
Algebraic & Geometric Topology 24 (2024) 4423–4469
DOI: 10.2140/agt.2024.24.4423
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 noncompact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided the surfaces are neither the plane nor the punctured plane. Thus all noncompact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense.

Keywords
topological rigidity, infinite-type surfaces, Dehn–Nielsen–Baer theorem
Mathematical Subject Classification
Primary: 57K20
Secondary: 55S37
References
Publication
Received: 26 June 2022
Revised: 21 May 2023
Accepted: 28 May 2023
Published: 17 December 2024
Authors
Sumanta Das
Department of Mathematics
Indian Institute of Science
Bangalore
India
© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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