A generating set for the palindromic Torelli group
| Autor: | Neil J. Fullarton |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Braid group
Group Theory (math.GR) automorphisms of free groups 01 natural sciences Combinatorics Mathematics - Geometric Topology Mathematics::Group Theory 0103 physical sciences FOS: Mathematics 20F65 0101 mathematics Mathematics Congruence subgroup Group (mathematics) 010102 general mathematics Geometric Topology (math.GT) Automorphism palindromes Mapping class group 57MXX Free group Generating set of a group 57M07 010307 mathematical physics Geometry and Topology Torelli groups Mathematics - Group Theory Word (group theory) |
| Zdroj: | Algebr. Geom. Topol. 15, no. 6 (2015), 3535-3567 |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2015.15.3535 |
| Popis: | A palindrome in a free group [math] is a word on some fixed free basis of [math] that reads the same backwards as forwards. The palindromic automorphism group [math] of the free group [math] consists of automorphisms that take each member of some fixed free basis of [math] to a palindrome; the group [math] has close connections with hyperelliptic mapping class groups, braid groups, congruence subgroups of [math] , and symmetric automorphisms of free groups. We obtain a generating set for the subgroup of [math] consisting of those elements that act trivially on the abelianisation of [math] , the palindromic Torelli group [math] . The group [math] is a free group analogue of the hyperelliptic Torelli subgroup of the mapping class group of an oriented surface. We obtain our generating set by constructing a simplicial complex on which [math] acts in a nice manner, adapting a proof of Day and Putman. The generating set leads to a finite presentation of the principal level 2 congruence subgroup of [math] . |
| Databáze: | OpenAIRE |
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