Comptes Rendus
Géométrie et Topologie
Surfaces of infinite-type are non-Hopfian
[Les surfaces de type infini sont non-Hopfian]
Sumanta Das1  ; Siddhartha Gadgil1
1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1349-1356.

Nous montrons que les surfaces de type fini sont caractérisées par un analogue topologique de la propriété de Hopf. A savoir, une surface orientée Σ est de type fini si et seulement si toute application propre f:Σ→Σ de degré un est homotope à un homéomorphisme.

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.

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DOI : 10.5802/crmath.504
Classification : 57K20, 55S37
Sumanta Das 1 ; Siddhartha Gadgil 1

1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Surfaces of infinite-type are {non-Hopfian}},
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Sumanta Das; Siddhartha Gadgil. Surfaces of infinite-type are non-Hopfian. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1349-1356. doi : 10.5802/crmath.504. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.504/

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