## Palindromic automorphisms of right-angled Artin groups

### Neil J. Fullarton and Anne Thomas

#### Abstract

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group $$A_\Gamma$$. The palindromic automorphism group $$\Pi A_\Gamma$$ is related to the principal congruence subgroups of $$\mathrm{GL}(n,\mathbb{Z})$$ and to the hyperelliptic mapping class group of an oriented surface, and sits inside the centraliser of a certain hyperelliptic involution in $$\mathrm{Aut}(A_\Gamma)$$. We obtain finite generating sets for $$\Pi A_\Gamma$$ and for this centraliser, and determine precisely when these two groups coincide. We also find generators for the palindromic Torelli group.

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 Monday, October 19, 2015