Title

Analysis of Length Spectra in the Complement of the Borromean Rings

Document Type

Student Presentation

Presentation Date

4-16-2018

College

College of Arts and Sciences

Department

Mathematics

Faculty Sponsor

Jens Harlander

Abstract

We study geodesics in the link complement B of the Borromean rings. Since B is covered by hyperbolic 3-space ℍ3 , the fundamental group of B is a discrete subgroup of the isometry group of ℍ3 , which is a matrix group. It follows that a geodesic gamma in B can be associated with a matrix M and the length of gamma can be computed using the trace of M. We use this technique to investigate the length spectrum of B and how it behaves under belt sum.

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