Year: 2024
Type: article
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.
Source: Algebraic & Geometric Topology
Author: Sumanta Das
Institution: Indian Institute of Science Bangalore
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405637295