arXiv Open Access 2021

Normal subgroups of big mapping class groups

Danny Calegari Lvzhou Chen

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Abstrak

Let S be a surface and let Mod(S,K) be the mapping class group of S permuting a Cantor subset K of S. We prove two structure theorems for normal subgroups of Mod(S,K). (Purity:) if S has finite type, every normal subgroup of Mod(S,K) either contains the kernel of the forgetful map to the mapping class group of S, or it is `pure', i.e. it fixes the Cantor set pointwise. (Inertia:) for any n element subset Q of the Cantor set, there is a forgetful map from the pure subgroup PMod(S,K) of Mod(S,K) to the mapping class group of (S,Q) fixing Q pointwise. If N is a normal subgroup of Mod(S,K) contained in PMod(S,K), its image N_Q is likewise normal. We characterize exactly which finite-type normal subgroups N_Q arise this way. Several applications and numerous examples are also given.

Topik & Kata Kunci

math.GT math.DS math.GR

Penulis (2)

Danny Calegari

Lvzhou Chen

Format Sitasi

APA MLA BibTeX

Calegari, D., Chen, L. (2021). Normal subgroups of big mapping class groups. https://arxiv.org/abs/2110.07839

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓