Surfaces of infinite-type are non-Hopfian
We show that finite-type surfaces are characterized by a topological analogue of the Hopf property. Namely, an oriented surface $\Sigma $ is of finite-type if and only if every proper map $f\colon \,\Sigma \rightarrow \Sigma $ of degree one is homotopic to a homeomorphism.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-10-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.504/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|