Paper Info
Title
Outer automorphism groups of free groups: linear and free representations.
Abstract
We study homomorphisms between Out(F-n) and Out(F-m) for n >= 6 and m <((n)(2)), and conclude that if m not equal n, then each such homomorphism factors through the finite group of order 2. In the course of the argument, linear representations of Out(F-n) in dimension less than ((n+1)(2)) over fields of characteristic zero are completely classified. It is shown that each such representation has to factor through the natural projection Out(F-n) -> GL(n)(Z) coming from the action of Out(F-n) on the abelianization of F-n. We obtain similar results for linear representation theory of Out(F-4) and Out(F-5).
Year
DOI
Venue
2013
10.1112/jlms/jds077
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Keywords
Field
DocType
group theory,free group
Topology,Outer automorphism group,Combinatorics,Mathematical analysis,Linear representation,Homomorphism,Finite group,Mathematics
Journal
Volume
Issue
ISSN
87
3
0024-6107
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Dawid Kielak100.68