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dc.contributor.authorHill, Michael
dc.date.accessioned2022-02-04T01:06:44Z
dc.date.available2022-02-04T01:06:44Z
dc.date.submitted2021-06-26
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/333633
dc.description.abstractWeidmann has produced a bound on the number of edges of a graph of groups splitting for when a finitely generated group acts on a tree (𝑘,𝐶)-acylindrically [25]. In the same paper Weidmann conjectures a common generalisation between their result and a theorem of Bestvina and Feighn [2]; which provides a similar bound for finitely generated groups acting on a tree with small edge stabilisers. We will produce an example which shows this conjecture is false. We then extend Weidmann’s result to actions which are 𝑘-acylindrical except on some set of subgroups with finite height. We then apply this result to a couple of specific cases. The first gives us a bound for actions of hyperbolic groups which are 𝑘-acylindrical on non virtually-cyclic subgroups. The second give a bound for a RAAG acting 𝑘-acylindrically on non-abelian subgroups. We also provide a sharp bound for finitely generated groups acting 𝑘-acylindrically. We also touch on the subject of strong accessibility. In particular we give an account of a theorem by Louder and Touikan [19] which shows that many hierarchies consisting of slender JSJ-decompositions are finite; in particular JSJ-hierarchies of 2-torsion-free hyperbolic groups are always finite.
dc.rightsAll Rights Reserved
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/
dc.subjectGroup Theory
dc.subjectGeometric Group Theory
dc.subjectBass-Serre Theory
dc.subjectAccessibility of Groups
dc.titleAcylindrical and strong accessibility
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.date.updated2022-02-03T16:05:13Z
dc.identifier.doi10.17863/CAM.81049
rioxxterms.licenseref.urihttps://www.rioxx.net/licenses/all-rights-reserved/
rioxxterms.typeThesis
dc.publisher.collegeSelwyn
pubs.funder-project-idEPSRC (1951087)
pubs.funder-project-idEngineering and Physical Sciences Research Council (1951087)
cam.supervisorWilton, Henry
cam.supervisor.orcidWilton, Henry [0000-0001-6369-9478]
cam.depositDate2022-02-03
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement


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