Cusp size bounds from singular surfaces in hyperbolic 3-manifolds Article

Adams, C, Colestock, A, Fowler, J et al. (2006). Cusp size bounds from singular surfaces in hyperbolic 3-manifolds . TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 358(2), 727-741. 10.1090/S0002-9947-05-03662-7

cited authors

  • Adams, C; Colestock, A; Fowler, J; Gillam, W; Katerman, E

authors

abstract

  • Singular maps of surfaces into a hyperbolic 3-manifold are utilized to find upper bounds on meridian length, ℓ-curve length and maximal cusp volume for the manifold. This allows a proof of the fact that there exist hyperbolic knots with arbitrarily small cusp density and that every closed orientable 3-manifold contains a knot whose complement is hyperbolic with maximal cusp volume less than or equal to 9. We also find particular upper bounds on meridian length, ℓ-curve length and maximal cusp volume for hyperbolic knots in S 3 depending on crossing number. Particular improved bounds are obtained for alternating knots. © 2005 American Mathematical Society.

publication date

  • February 1, 2006

published in

Digital Object Identifier (DOI)

start page

  • 727

end page

  • 741

volume

  • 358

issue

  • 2