Palindromic automorphisms of right-angled Artin groups

Abstract

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

20 pages, 2 figures. Version 2: corrected proof of Proposition 3.1, other minor changes as suggested by referee. To appear in Groups Geom. Dyn