Surfaces of infinite-type are non-Hopfian
Geometric Topology
2023-06-07 v2 Algebraic Topology
Abstract
We show that finite-type surfaces are characterized by a topological analog of the Hopf property. Namely, an oriented surface is of finite-type if and only if every proper map of degree one is homotopic to a homeomorphism.
Keywords
Cite
@article{arxiv.2210.03395,
title = {Surfaces of infinite-type are non-Hopfian},
author = {Sumanta Das and Siddhartha Gadgil},
journal= {arXiv preprint arXiv:2210.03395},
year = {2023}
}
Comments
8 pages, 4 figures. v2: incorporates the referee's comments, accepted in the Comptes Rendus Math\'ematique