Every L-space knot is fibered and strongly quasi-positive, but this does not hold for L-space links. In this paper, we use the so called H-function, which is a concordance link invariant, to introduce a subfamily of fibered strongly quasi-positive L-space links. Furthermore, we present an infinite family of L-space links which are not quasi-positive.
We show convergence of small eigenvalues for geometrically finite hyperbolic n-manifolds under strong limits. For a class of convergent convex sets in a strongly convergent sequence of Kleinian groups, we use the spectral gap of the limit manifold and the exponentially mixing property of the geodesic flow along the strongly convergent sequence to find asymptotically uniform counting formulas for the number of orthogeodesics between the convex sets. In particular, this provides asymptotically uniform counting formulas (with respect to length) for orthogeodesics between converging Margulis tubes, geodesic loops based at converging basepoints, and primitive closed geodesics.
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