Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 6 (2015), 3535-3567.
A generating set for the palindromic Torelli group
A palindrome in a free group is a word on some fixed free basis of that reads the same backwards as forwards. The palindromic automorphism group of the free group consists of automorphisms that take each member of some fixed free basis of to a palindrome; the group has close connections with hyperelliptic mapping class groups, braid groups, congruence subgroups of , and symmetric automorphisms of free groups. We obtain a generating set for the subgroup of consisting of those elements that act trivially on the abelianisation of , the palindromic Torelli group . The group 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 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 .
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3535-3567.
Received: 4 November 2014
Revised: 14 April 2015
Accepted: 19 April 2015
First available in Project Euclid: 16 November 2017
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Fullarton, Neil J. A generating set for the palindromic Torelli group. Algebr. Geom. Topol. 15 (2015), no. 6, 3535--3567. doi:10.2140/agt.2015.15.3535. https://projecteuclid.org/euclid.agt/1510841076