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Bregman, Corey, Charney, Ruth and Vogtmann, Karen (2023) Outer space for RAAGs. Duke Mathematical Journal, 172 (6). pp. 1033-1108. doi:10.1215/00127094-2023-0007 ISSN 0012-7094.
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Official URL: https://doi.org/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 properly. 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 R n 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.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Geometric group theory, Lie groups, Lattice theory, Automorphisms, Outer space, Metric spaces, Homeomorphisms, Isomorphisms (Mathematics) | |||||||||
Journal or Publication Title: | Duke Mathematical Journal | |||||||||
Publisher: | Duke University Press | |||||||||
ISSN: | 0012-7094 | |||||||||
Official Date: | 15 April 2023 | |||||||||
Dates: |
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Volume: | 172 | |||||||||
Number: | 6 | |||||||||
Number of Pages: | 61 | |||||||||
Page Range: | pp. 1033-1108 | |||||||||
DOI: | 10.1215/00127094-2023-0007 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © 2023 Duke University Press | |||||||||
Date of first compliant deposit: | 19 April 2022 | |||||||||
Date of first compliant Open Access: | 20 April 2022 | |||||||||
RIOXX Funder/Project Grant: |
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