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.
TETRAHEDRON MANIFOLD SERIES OF HEEGAARD GENUS TWO WITH KNOT PRESENTATION AND DEHN SURGERY / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: ACTA MATHEMATICA HUNGARICA. - ISSN 0236-5294. - ELETTRONICO. - 131:4(2011), pp. 307-322. [10.1007/s10474-010-0001-2]
TETRAHEDRON MANIFOLD SERIES OF HEEGAARD GENUS TWO WITH KNOT PRESENTATION AND DEHN SURGERY
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2011
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.
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