Abstract
In [13] the second named author and Yamashita defined the link volume, an invariant of closed orientable 3–manifolds that measures how efficiently a given manifold can be represented as a branched cover of S . We use the notation M d ! .S;L/ to denote a covering projection from M to S , branched along L and of degree d . We restrict to the case where L is a hyperbolic link. Then the complexity of M d ! .S;L/ is defined to be d Vol.S nL/, that is, the degree of the cover times the volume of the complement of the branch set. The link volume of a closed orientable 3–manifold M is denoted LinkVol.M / and defined to be the infimum of the complexities of all covers (of all possible degrees) M d ! .S;L/, that is,
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