Tetrahedron manifold series of Heegaard genus two with knot presentation and Dehn surgery

Abstract

We construct a 2-parametric family of tetrahedron manifolds, mainly with hyperbolic structure. We give geometric presentations of their fundamental groups with two generators. Furthermore, we show that the constructed manifolds are 2-fold coverings of the 3-sphere branched over specified knots, and give a surgery description of them.