{"title":"无限型曲面是非hopfian曲面","authors":"Sumanta Das, Siddhartha Gadgil","doi":"10.5802/crmath.504","DOIUrl":null,"url":null,"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.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"101 24","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Surfaces of infinite-type are non-Hopfian\",\"authors\":\"Sumanta Das, Siddhartha Gadgil\",\"doi\":\"10.5802/crmath.504\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":10620,\"journal\":{\"name\":\"Comptes Rendus Mathematique\",\"volume\":\"101 24\",\"pages\":\"0\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/crmath.504\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/crmath.504","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
期刊介绍：
The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English.
The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.
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