非平面末端持续令人难忘

arXiv - MATH - Group Theory Pub Date : 2024-09-09 DOI:arxiv-2409.05502

Javier Aramayona, Rodrigo De Pool, Rachel Skipper, Jing Tao, Nicholas G. Vlamis, Xiaolei Wu

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引用次数: 0

摘要

我们证明了无平面末端的可定向无限属 2-manifolds的映射类群的一类子群之间的连续外变形总是由同态诱导的。该类子群包括纯映射类群、紧凑支撑映射类群的闭包，以及在底层流形有无限多个端点或完全自相似的情况下的全映射类群。作为推论，这些群都是霍普菲拓扑群。

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Non-planar ends are continuously unforgettable

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.

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arXiv - MATH - Group Theory

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