Fundamental Group and Covering Properties of Hyperbolic Surgery Manifolds. (30th September 2013) - Cavicchioli, Alberto; Spaggiari, Fulvia; Telloni, Agnese Ilaria
Abstract : We study a family of closed connected orientable 3-manifolds obtained by Dehn surgeries with rational coefficients along the oriented components of certain links. This family contains all the manifolds obtained by surgery along the (hyperbolic) 2-bridge knots. We find geometric presentations for the fundamental group of such manifolds and represent them as branched covering spaces. As a consequence, we prove that the surgery manifolds, arising from the hyperbolic 2-bridge knots, have Heegaard genus 2 and are 2-fold coverings of the 3-sphere branched over well-specified links.