Volume 21, issue 6 (2021)

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Alternating links with totally geodesic checkerboard surfaces

Hong-Chuan Gan

Algebraic & Geometric Topology 21 (2021) 3107–3122
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
Primary: 57M50
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