15 April 2023 Outer space for RAAGs
Corey Bregman, Ruth Charney, Karen Vogtmann
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Duke Math. J. 172(6): 1033-1108 (15 April 2023). DOI: 10.1215/00127094-2023-0007

Abstract

For any right-angled Artin group AΓ, we construct a finite-dimensional space OΓ on which the group Out(AΓ) of outer automorphisms of AΓ acts with finite point stabilizers. We prove that OΓ is contractible, so that the quotient is a rational classifying space for Out(AΓ). The space OΓ blends features of the symmetric space of lattices in Rn with those of outer space for the free group Fn. Points in OΓ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with AΓ.

Citation

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Corey Bregman. Ruth Charney. Karen Vogtmann. "Outer space for RAAGs." Duke Math. J. 172 (6) 1033 - 1108, 15 April 2023. https://doi.org/10.1215/00127094-2023-0007

Information

Received: 18 September 2020; Revised: 19 February 2022; Published: 15 April 2023
First available in Project Euclid: 3 April 2023

MathSciNet: MR4576238
zbMATH: 07684361
Digital Object Identifier: 10.1215/00127094-2023-0007

Subjects:
Primary: 20F28
Secondary: 20F36 , 20F65

Keywords: automorphism groups , Outer space , right-angled Artin group

Rights: Copyright © 2023 Duke University Press

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Vol.172 • No. 6 • 15 April 2023
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