dc.creator | Minasyan, Ashot | |
dc.date.accessioned | 2020-08-22T00:26:24Z | |
dc.date.available | 2006-06-29 | |
dc.date.issued | 2005-06-29 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-04062005-201041 | |
dc.identifier.uri | http://hdl.handle.net/1803/12025 | |
dc.description.abstract | A geodesic metric space $X$ is called hyperbolic if there exists $delta ge 0$ such that
every geodesic triangle $Delta$ in $X$ is $delta$-slim, i.e., each side of $Delta$ is contained
in a closed $delta$-neighborhood of the two other sides. Let $G$ be a group generated by a finite set $A$
and let $Gamma$ be the corresponding Cayley graph. The group $G$ is said to be word hyperbolic if $Gamma$ is a hyperbolic
metric space. A subset $Q$ of the group $G$ is called quasiconvex if for any geodesic $gamma$ connecting
two elements from $Q$ in $Gamma$, $gamma$ is contained in a closed $varepsilon$-neighborhood of $Q$ (for some fixed
$varepsilon ge 0$). Quasiconvex subgroups play an important role in the theory of hyperbolic groups and have been
studied quite thoroughly.
We investigate properties of quasiconvex subsets in word hyperbolic groups and generalize a number of results
previously known about quasiconvex subgroups. On the other hand, we establish and study a notion of quasiconvex subsets
that are small relatively to subgroups. This allows to prove a theorem concerning residualizing homomorphisms
preserving such subsets. As corollaries, we obtain several new embedding theorems for word hyperbolic groups. | |
dc.format.mimetype | application/pdf | |
dc.subject | geometric group theory | |
dc.title | On Quasiconvex Subsets of Hyperbolic Groups | |
dc.type | dissertation | |
dc.contributor.committeeMember | Tom Kephart | |
dc.contributor.committeeMember | Bruce Hughes | |
dc.contributor.committeeMember | Mike Mihalik | |
dc.contributor.committeeMember | Mark Sapir | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2006-06-29 | |
local.embargo.lift | 2006-06-29 | |
dc.contributor.committeeChair | Alexander Olshanskiy | |