Right-angled Artin groups as normal subgroups of mapping class groups
| Autor: | Dan Margalit, Matt Clay, Johanna Mangahas |
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| Rok vydání: | 2020 |
| Předmět: |
Normal subgroup
Class (set theory) Algebra and Number Theory 010102 general mathematics Braid group Closure (topology) Geometric Topology (math.GT) Group Theory (math.GR) 01 natural sciences Mapping class group Combinatorics 57K20 57M07 20F65 Mathematics - Geometric Topology Group action Mathematics::Group Theory Projection (mathematics) 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics - Group Theory Congruence subgroup Mathematics |
| DOI: | 10.48550/arxiv.2001.10587 |
| Popis: | We construct the first examples of normal subgroups of mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, non-free right-angled Artin subgroups of other groups, such as braid groups and pure braid groups, as well as many subgroups of the mapping class group, such as the Torelli subgroup. Our work recovers and generalizes the seminal result of Dahmani-Guirardel-Osin, which gives free, purely pseudo-Anosov normal subgroups of mapping class groups. We give two applications of our methods: (1) we produce an explicit proper normal subgroup of the mapping class group that is not contained in any level $m$ congruence subgroup, and (2) we produce an explicit example of a pseudo-Anosov mapping class with the property that all of its even powers have free normal closure and its odd powers normally generate the entire mapping class group. The technical theorem at the heart of our work is a new version of the windmill apparatus of Dahmani-Guirardel-Osin, which is tailored to the setting of group actions on the projection complexes of Bestvina-Bromberg-Fujiwara. Comment: 40 pages, 8 figures; v2: incorporates comments from referee; v3: minor edits, final version |
| Databáze: | OpenAIRE |
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