Non-planar ends are continuously unforgettable
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866911421994893312 |
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| author | Aramayona, Javier De Pool, Rodrigo Skipper, Rachel Tao, Jing Vlamis, Nicholas G. Wu, Xiaolei |
| author_facet | Aramayona, Javier De Pool, Rodrigo Skipper, Rachel Tao, Jing Vlamis, Nicholas G. Wu, Xiaolei |
| contents | We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group, the closure of the compactly supported mapping classes, and the full mapping class group in the case that the underlying manifold has a finite number of ends or is perfectly self-similar. As a corollary, these groups are Hopfian topological groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-planar ends are continuously unforgettable Aramayona, Javier De Pool, Rodrigo Skipper, Rachel Tao, Jing Vlamis, Nicholas G. Wu, Xiaolei Geometric Topology Group Theory We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group, the closure of the compactly supported mapping classes, and the full mapping class group in the case that the underlying manifold has a finite number of ends or is perfectly self-similar. As a corollary, these groups are Hopfian topological groups. |
| title | Non-planar ends are continuously unforgettable |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2409.05502 |