Journal article
Outer actions of Out (Fn) on small right-angled Artin groups
- Abstract:
- We determine the precise conditions under which SOut(Fn), the unique index-two subgroup of Out(Fn), can act nontrivially via outer automorphisms on a RAAG whose defining graph has fewer than 12(n2) vertices. We also show that the outer automorphism group of a RAAG cannot act faithfully via outer automorphisms on a RAAG with a strictly smaller (in number of vertices) defining graph. Along the way we determine the minimal dimensions of nontrivial linear representations of congruence quotients of the integral special linear groups over algebraically closed fields of characteristic zero, and provide a new lower bound on the cardinality of a set on which SOut(Fn) can act nontrivially.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, 230.9KB, Terms of use)
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- Publisher copy:
- 10.2140/agt.2018.18.1041
Authors
- Publisher:
- Mathematical Sciences Publishers
- Journal:
- Algebraic & Geometric Topology More from this journal
- Volume:
- 18
- Issue:
- 2
- Pages:
- 1041-1065
- Publication date:
- 2018-03-12
- Acceptance date:
- 2017-11-21
- DOI:
- EISSN:
-
1472-2739
- ISSN:
-
1472-2747
Terms of use
- Copyright holder:
- Mathematical Sciences Publishers
- Copyright date:
- 2018
- Rights statement:
- © Copyright 2018 Mathematical Sciences Publishers. All rights reserved.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Mathematical Sciences Publishers at: https://doi.org/10.2140/agt.2018.18.1041
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