Faculty Publications
Publication Date
2017
Disciplines
Geometry and Topology | Mathematics
Abstract
In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurability classes by analyzing their cusp shapes.
The knot complements in each class differ by a topological cut-and-paste operation known as mutation. Ruberman has shown that mutations of hyperelliptic surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide geometric and topological conditions under which such mutations also preserve the initial (complex) length spectrum. This work requires us to analyze when least area surfaces could intersect short geodesics in a hyperbolic 3-manifold.
Document Type
Published Version
Rights
First published in Communications in Analysis and Geometry in volume 25, issue 3, published by International Press.
Original Citation
Christian Millichap
Mutations and short geodesics in hyperbolic 3-manifolds.
Communications in Analysis and Geometry, 2017, volume 25, issue 3, pages 625-683
doi:10.4310/CAG.2017.v25.n3.a5
DigitalCommons@Linfield Citation
Millichap, Christian, "Mutations and Short Geodesics in Hyperbolic 3-Manifolds" (2017). Faculty Publications. Published Version. Submission 11.
https://digitalcommons.linfield.edu/mathfac_pubs/11
Comments
This article is the publisher-created version, also considered to be the final version or the version of record. It includes value-added elements provided by the publisher, such as copy editing, layout changes, and branding consistent with the rest of the publication.