We show that finite-type surfaces are characterized by a topological analogue 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.
Nous montrons que les surfaces de type fini sont caractérisées par un analogue topologique de la propriété de Hopf. A savoir, une surface orientée est de type fini si et seulement si toute application propre de degré un est homotope à un homéomorphisme.
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Sumanta Das 1; Siddhartha Gadgil 1
@article{CRMATH_2023__361_G8_1349_0, author = {Sumanta Das and Siddhartha Gadgil}, title = {Surfaces of infinite-type are {non-Hopfian}}, journal = {Comptes Rendus. Math\'ematique}, pages = {1349--1356}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.504}, language = {en}, }
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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