Show simple item record

dc.contributor.advisorShalen, Peter B.en_US
dc.contributor.authorSiler, William M.en_US
dc.date.accessioned2013-06-28T17:26:34Z
dc.date.available2013-06-28T17:26:34Z
dc.date.created2013-05en_US
dc.date.issued2013-06-28
dc.date.submitted2013-05en_US
dc.identifier.urihttp://hdl.handle.net/10027/9909
dc.description.abstractA carrier graph is a map from a finite graph to a hyperbolic 3-manifold M, which is surjective on the level of fundamental groups. We can pull back the metric on M to get a notion of length for the graph. We study the geometric properties of the carrier graphs with minimal possible length. We show that minimal length carrier graphs exist for a large class of 3-manifolds. We also show that those manifolds have only finitely many minimal length carrier graphs, from which we deduce a new proof that such manifolds have finite isometry groups. Finally, we give a theorem relating lengths of loops in a minimal length carrier graph to the lengths of its edges. From this we are able, for example, to get an explicit upper bound on the injectivity radius of M based on the lengths of edges in a minimal length carrier graph.en_US
dc.language.isoenen_US
dc.rightsCopyright 2013 William M. Sileren_US
dc.subjecthyperbolic geometryen_US
dc.subject3-manifolden_US
dc.subjectcarrier graphen_US
dc.titleThe Geometry of Carrier Graphs in Hyperbolic 3-Manifoldsen_US
thesis.degree.departmentMathematics, Statistics, and Computer Scienceen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Illinois at Chicagoen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePhD, Doctor of Philosophyen_US
dc.type.genrethesisen_US
dc.contributor.committeeMemberGroves, Danielen_US
dc.contributor.committeeMemberCuller, Marcen_US
dc.contributor.committeeMemberDumas, Daviden_US
dc.contributor.committeeMemberFarb, Bensonen_US
dc.type.materialtexten_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record