dc.creator | Sun, Bin | |
dc.date.accessioned | 2020-08-22T00:41:24Z | |
dc.date.available | 2019-05-24 | |
dc.date.issued | 2019-05-24 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-05122019-221719 | |
dc.identifier.uri | http://hdl.handle.net/1803/12295 | |
dc.description.abstract | This thesis aims to study cohomology of group theoretic Dehn fillings. For sufficiently deep Dehn fillings of hyperbically embedded subgroups, we first prove that Dehn filling kernels enjoy a particular free product structure, which is termed the Cohen-Lyndon property. We then combine the Cohen-Lyndon property with the Lyndon-Hochschild-Serre spectral sequence to compute cohomology of Dehn filling quotients. As applications, we estimate cohomological dimensions of Dehn fillings quotients, give criterions for Dehn fillings quotients to be of type $FP_{infty}$, and construct useful quotients of acylindrically hyperbolic groups with certain homological properties. | |
dc.format.mimetype | application/pdf | |
dc.subject | hyperbolically embedded subgroup | |
dc.subject | group theoretic Dehn filling | |
dc.subject | group cohomology | |
dc.title | Cohomology of group theoretic Dehn fillings | |
dc.type | dissertation | |
dc.contributor.committeeMember | Michael Mihalik | |
dc.contributor.committeeMember | Alexander Olshanskiy | |
dc.contributor.committeeMember | Robert Scherrer | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2019-05-24 | |
local.embargo.lift | 2019-05-24 | |
dc.contributor.committeeChair | Denis Osin | |