All Dehn Fillings of the Whitehead Link Complement are Tetrahedron Manifolds

Year 2022, Volume: 15 Issue: 2, 192 - 201, 31.10.2022

Alberto Cavicchioli , Fulvia Spaggiari

https://doi.org/10.36890/iejg.1102753

Abstract

In this paper we show that Dehn surgeries on the oriented components of the Whitehead link yield tetrahedron manifolds of Heegaard genus $\le 2$. As a consequence, the eight homogeneous Thurston 3-geometries are realized by tetrahedron manifolds of Heegaard genus $\le 2$. The proof is based on techniques of Combinatorial Group Theory, and geometric presentations of manifold fundamental groups.

Keywords

Tetrahedron manifold, Whitehead link, Dehn surgery, Heegaard genus, group presentation

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