All Dehn Fillings of the Whitehead Link Complement are Tetrahedron Manifolds

Authors : Alberto CAVİCCHİOLİ, Fulvia SPAGGİARİ

Pages : 192-201

Doi:10.36890/iejg.1102753

View : 10 | Download : 6

Publication Date : 2022-10-31

Article Type : Research Paper

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