Document Type
Topology + Dynamics and Continuum Theory
Publication Date
6-2017
Publication Source
32nd Summer Conference on Topology and Its Applications
Abstract
The Seifert conjecture was answered negatively in 1994 by Kuperberg who constructed a smooth aperiodic flow on a three-manifold. This construction was later found to contain a minimal set with a complicated topology. The minimal set is embedded as a lamination by surfaces with a Cantor transversal of Lebesgue measure zero. In this talk we will discuss the pseudogroup dynamics on the transversal, the induced symbolic dynamics, and the Hausdorff dimension of the Cantor set.
Copyright
Copyright © 2017, the Author
eCommons Citation
Ingbretson, Daniel, "Hausdorff Dimension of Kuperberg Minimal Sets" (2017). Summer Conference on Topology and Its Applications. 9.
https://ecommons.udayton.edu/topology_conf/9
Comments
This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.
Technological limitations may prevent some mathematical symbols and functions from displaying correctly in this record’s metadata fields. Please refer to the attached PDF for the correct display.