Centralisers of polynomially growing automorphisms of free groups
Centralisers of polynomially growing automorphisms of free groups
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DissertationDate of Exam
02.07.2013Date of Publication
31.07.2013Advisor
Bödigheimer, Carl-FriedrichCo-Referee
Bridson, MartinMetadata
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Abstract
The main theorem of this thesis asserts that many centralisers in the automorphism groups Aut(F_n) and Out(F_n) of the free group F_n satisfy finiteness property VF, i.e. these centralisers have a finite index subgroup with a finite polyhedron as a classifying space. I first introduce higher graphs of groups and their automorphisms, which generalise the well-known graphs of groups. Important automorphisms are higher Dehn twists. I then use the structure of the automorphism group of the higher graph of groups to show that centralisers of higher Dehn twist automorphisms in Out(F_n) and Aut(F_n) are of type VF. This includes all polynomially growing automorphisms up to passing to powers. Finally, I compute explicit abelianisations of some centralisers, which give information on translation lengths in isometric CAT(0) actions.
Subjects
Automorphismus, freie Gruppe, geometrische Gruppentheorie, klassifizierender Raum, Zentralisator, CAT(0), graph of groups
Classification (DDC)
510 MathematikRodenhausen, Moritz: Centralisers of polynomially growing automorphisms of free groups. - Bonn, 2013. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-32944
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-32944
@phdthesis{handle:20.500.11811/5725,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-32944,
author = {{Moritz Rodenhausen}},
title = {Centralisers of polynomially growing automorphisms of free groups},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = jul,
note = {The main theorem of this thesis asserts that many centralisers in the automorphism groups Aut(F_n) and Out(F_n) of the free group F_n satisfy finiteness property VF, i.e. these centralisers have a finite index subgroup with a finite polyhedron as a classifying space. I first introduce higher graphs of groups and their automorphisms, which generalise the well-known graphs of groups. Important automorphisms are higher Dehn twists. I then use the structure of the automorphism group of the higher graph of groups to show that centralisers of higher Dehn twist automorphisms in Out(F_n) and Aut(F_n) are of type VF. This includes all polynomially growing automorphisms up to passing to powers. Finally, I compute explicit abelianisations of some centralisers, which give information on translation lengths in isometric CAT(0) actions.},
url = {https://hdl.handle.net/20.500.11811/5725}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-32944,
author = {{Moritz Rodenhausen}},
title = {Centralisers of polynomially growing automorphisms of free groups},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = jul,
note = {The main theorem of this thesis asserts that many centralisers in the automorphism groups Aut(F_n) and Out(F_n) of the free group F_n satisfy finiteness property VF, i.e. these centralisers have a finite index subgroup with a finite polyhedron as a classifying space. I first introduce higher graphs of groups and their automorphisms, which generalise the well-known graphs of groups. Important automorphisms are higher Dehn twists. I then use the structure of the automorphism group of the higher graph of groups to show that centralisers of higher Dehn twist automorphisms in Out(F_n) and Aut(F_n) are of type VF. This includes all polynomially growing automorphisms up to passing to powers. Finally, I compute explicit abelianisations of some centralisers, which give information on translation lengths in isometric CAT(0) actions.},
url = {https://hdl.handle.net/20.500.11811/5725}
}
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