Strong topological rigidity of noncompact orientable surfaces

Das, Sumanta

doi:10.2140/agt.2024.24.4423

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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

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Volume 24, issue 8 (2024)