Return to search

Unknotting Tunnels of Hyperbolic Tunnel Number n Manifolds

Adams conjectured that unknotting tunnels of tunnel number 1 manifolds are always isotopic to a geodesic. We generalize this question to tunnel number n manifolds. We find that there exist complete hyperbolic structures and a choice of spine of a compression body with genus 1 negative boundary and genus n ≥ 3 outer boundary for which (n−2) edges of the spine self-intersect. We use this to show that there exist finite volume one-cusped hyperbolic manifolds with a system of n tunnels for which (n−1) of the tunnels are homotopic to geodesics arbitrarily close to self-intersecting. This gives evidence that the generalization of Adam's conjecture to tunnel number n ≥ 2 manifolds may be false.

Identiferoai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-4306
Date02 July 2012
CreatorsBurton, Stephan Daniel
PublisherBYU ScholarsArchive
Source SetsBrigham Young University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceAll Theses and Dissertations
Rightshttp://lib.byu.edu/about/copyright/

Page generated in 0.0021 seconds