On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups
On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups
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DissertationDate of Exam
25.06.2018Date of Publication
20.07.2018Advisor
Lück, WolfgangCo-Referee
Leary, Ian J.Metadata
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Abstract
This thesis mainly deals with finiteness properties of the classifying space for the family of virtually cyclic subgroups. We establish a link between the finiteness of the classifying space and the conjugacy growth invariant of the given group and use this connection to show that the classifying space for virtually cyclic subgroups is not of finite type except in trivial cases if the group is linear or a CAT(0) cube group. We also investigate the class of residually finite groups in this context and along the way come close to a classification of the finite groups which have only two conjugacy classes of maximal cyclic subgroups.
Subjects
Mathematik, Algebraische Topologie, Gruppentheorie, Klassifizierender Raum, Konjugationsklasse, mathematics, algebraic topology, group theory, classifying space, conjugacy class
Classification (DDC)
510 Mathematikvon Puttkamer, Timm Wilhelm: On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups. - Bonn, 2018. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-51511
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-51511
@phdthesis{handle:20.500.11811/7608,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-51511,
author = {{Timm Wilhelm von Puttkamer}},
title = {On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2018,
month = jul,
note = {This thesis mainly deals with finiteness properties of the classifying space for the family of virtually cyclic subgroups. We establish a link between the finiteness of the classifying space and the conjugacy growth invariant of the given group and use this connection to show that the classifying space for virtually cyclic subgroups is not of finite type except in trivial cases if the group is linear or a CAT(0) cube group. We also investigate the class of residually finite groups in this context and along the way come close to a classification of the finite groups which have only two conjugacy classes of maximal cyclic subgroups.},
url = {https://hdl.handle.net/20.500.11811/7608}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-51511,
author = {{Timm Wilhelm von Puttkamer}},
title = {On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2018,
month = jul,
note = {This thesis mainly deals with finiteness properties of the classifying space for the family of virtually cyclic subgroups. We establish a link between the finiteness of the classifying space and the conjugacy growth invariant of the given group and use this connection to show that the classifying space for virtually cyclic subgroups is not of finite type except in trivial cases if the group is linear or a CAT(0) cube group. We also investigate the class of residually finite groups in this context and along the way come close to a classification of the finite groups which have only two conjugacy classes of maximal cyclic subgroups.},
url = {https://hdl.handle.net/20.500.11811/7608}
}
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