Surfaces of infinite-type are non-Hopfian

Sumanta Das, Siddhartha Gadgil

Type: Article

Publication Date: 2023-10-31

Citations: 0

DOI: https://doi.org/10.5802/crmath.504

Abstract

We show that finite-type surfaces are characterized by a topological analogue of the Hopf property. Namely, an oriented surface Σ is of finite-type if and only if every proper map f:Σ→Σ of degree one is homotopic to a homeomorphism.

Locations

Comptes Rendus Mathématique - View - PDF
arXiv (Cornell University) - View - PDF
ePrints@IISc (Indian Institute of Science) - View - PDF

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+	Geometric Topology in Dimensions 2 and 3	1977	Edwin E. Moïse
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+	Curves on 2-manifolds and isotopies	1966	D. B. A. Epstein
+ PDF Chat	On the Classification of Noncompact Surfaces	1963	Ian Richards
+ PDF Chat	Residual Finiteness of Surface Groups	1972	J Hempel
+ PDF Chat	Homeomorphic subsurfaces and the omnipresent arcs	2021	Federica Fanoni Tyrone Ghaswala Alan McLeay