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

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.

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hyperbolic geometry, alternating link, totally geodesic surface, right-angled polyhedron
Mathematical Subject Classification
Primary: 57M50
Received: 24 May 2020
Revised: 5 October 2020
Accepted: 20 October 2020
Published: 22 November 2021
Hong-Chuan Gan
Department of Mathematics
Sun Yat-sen University