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Free and linear representations of outer automorphism groups of free groups

Abstract:

For various values of n and m we investigate homomorphisms from Out(F_n) to Out(F_m) and from Out(F_n) to GL_m(K), i.e. the free and linear representations of Out(F_n) respectively.

By means of a series of arguments revolving around the representation theory of finite symmetric subgroups of Out(F_n) we prove that each homomorphism from Out(F_n) to GL_m(K) factors through the natural map p_n from Out(F_n) to GL(H_1(F_n,Z)) = GL_n(Z) whenever n=3, m < 7 and char(K) is not an elemen...

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Institution:
University of Oxford
Research group:
Topology
Oxford college:
Magdalen College
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute

Contributors

Role:
Supervisor
Publication date:
2012
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
Oxford University, UK
URN:
uuid:f2045fba-1546-4dd3-af9f-7d02c4fc505e
Local pid:
ora:6710

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