JournalsggdVol. 12, No. 3pp. 865–887

Palindromic automorphisms of right-angled Artin groups

  • Neil J. Fullarton

    Rice University, Houston, USA
  • Anne Thomas

    University of Sydney, Australia
Palindromic automorphisms of right-angled Artin groups cover
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Abstract

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group AΓA_\Gamma. The palindromic automorphism group ΠAΓ\Pi A_\Gamma is related to the principal congruence subgroups of GL(n,Z)(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 Aut(AΓ)(A_\Gamma). We obtain finite generating sets for ΠAΓ\Pi A_\Gamma and for this centraliser, and determine precisely when these two groups coincide. We also find generators for the palindromic Torelli group.

Cite this article

Neil J. Fullarton, Anne Thomas, Palindromic automorphisms of right-angled Artin groups. Groups Geom. Dyn. 12 (2018), no. 3, pp. 865–887

DOI 10.4171/GGD/458