Alternating links with totally geodesic checkerboard surfaces

Gan, Hong-Chuan

doi:10.2140/agt.2021.21.3107

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Alternating links with totally geodesic checkerboard surfaces

Hong-Chuan Gan

Algebraic & Geometric Topology 21 (2021) 3107–3122

DOI: 10.2140/agt.2021.21.3107

Abstract

We prove that alternating links with two totally geodesic checkerboard surfaces are three links with projection the $1$ –skeleton of the octahedron, the cuboctahedron and the icosidodecahedron. Then we characterize these links as right-angled completely realizable links and show that all hyperbolic weaving knots with two exceptions have both checkerboard surfaces not totally geodesic.

Keywords

hyperbolic geometry, alternating link, totally geodesic surface, right-angled polyhedron

Mathematical Subject Classification

Primary: 57M50

References

Publication

Received: 24 May 2020

Revised: 5 October 2020

Accepted: 20 October 2020

Published: 22 November 2021

Authors

Hong-Chuan Gan
Department of Mathematics Sun Yat-sen University Guangzhou China

Volume 21, issue 6 (2021)