Analysis of Length Spectra in the Complement of the Borromean Rings
College of Arts and Sciences
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.
Neal, Kayla, "Analysis of Length Spectra in the Complement of the Borromean Rings" (2018). 2018 Undergraduate Research and Scholarship Conference. 107.