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.
Highlights
As well known, any closed connected orientable 3-manifold can be obtained by Dehn surgeries on the components of an oriented link in the 3-sphere
Any closed connected orientable 3-manifold can be obtained by Dehn surgeries on the components of an oriented link in the 3-sphere. If such a link is hyperbolic, the Thurston-Jorgensen theory [3] of hyperbolic surgery implies that the resulting manifolds are hyperbolic for almost all surgery coefficients
In the context of current research in 3-manifold topology, many classes of closed orientable hyperbolic 3-manifolds have been constructed by considering branched coverings of links or by performing Dehn surgery along them
Summary
Any closed connected orientable 3-manifold can be obtained by Dehn surgeries on the components of an oriented link in the 3-sphere (see [1, 2]). The closed manifold Mn(ri/si; pi/qi; h/k) admits a Heegaard diagram of genus 2n + 1 inducing the above presentation, which is geometric.
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