Communications in Analysis and Geometry

Volume 31 (2023)

Number 3

Embedded totally geodesic surfaces in fully augmented links

Pages: 563 – 593

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n3.a2

Authors

Sierra Knavel (Department of Mathematics, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Rolland Trapp (Department of Mathematics, California State University, San Bernardino, Calif., U.S.A.)

Abstract

This paper studies embedded totally geodesic surfaces in fully augmented link complements. Not surprisingly, there are no closed embedded totally geodesic surfaces. Non-compact surfaces disjoint from crossing disks are seen to be punctured spheres orthogonal to the standard cell decomposition, while those that intersect crossing disks do so in very restricted ways. Finally we show there is an augmentation of any checkerboard surface in which that surface becomes totally geodesic.

Full Text (PDF format)

Received 22 May 2020

Accepted 8 December 2020

Published 4 January 2024