Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Entire DC Network
Nonlocally Maximal Hyperbolic Sets For Flows, Taylor Michael Petty
Nonlocally Maximal Hyperbolic Sets For Flows, Taylor Michael Petty
Theses and Dissertations
In 2004, Fisher constructed a map on a 2-disc that admitted a hyperbolic set not contained in any locally maximal hyperbolic set. Furthermore, it was shown that this was an open property, and that it was embeddable into any smooth manifold of dimension greater than one. In the present work we show that analogous results hold for flows. Specifically, on any smooth manifold with dimension greater than or equal to three there exists an open set of flows such that each flow in the open set contains a hyperbolic set that is not contained in a locally maximal one.
Statistical Hyperbolicity Of Relatively Hyperbolic Groups, Jeremy Osborne
Statistical Hyperbolicity Of Relatively Hyperbolic Groups, Jeremy Osborne
Theses and Dissertations
In this work, we begin by defining what it means for a group to be statistically hyperbolic. We then give several examples of groups, including non-elementary hyperbolic groups, which either are statistically hyperbolic or are not. Following that, we define what it means for a group to be relatively hyperbolic. Finally, in the main portion of this work, we show that groups which are relatively hyperbolic, with a few additional conditions in place, must also be statistically hyperbolic.
A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson
A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson
Theses and Dissertations
The hyperbolic volume of a knot complement is a topological knot invariant. Futer, Kalfagianni, and Purcell have estimated the volumes of Montesinos link complements for Montesinos links with at least three positive tangles. Here we extend their results to all hyperbolic Montesinos links.
Subdivision Rules, 3-Manifolds, And Circle Packings, Brian Craig Rushton
Subdivision Rules, 3-Manifolds, And Circle Packings, Brian Craig Rushton
Theses and Dissertations
We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to …