63,602 research outputs found
Finite type invariants of integral homology 3-spheres: A survey
This is a survey on the current status of the study of finite type invariants
of integral homology 3-spheres based on lectures given in the workshop on knot
theory at Banach International Center of Mathematics, Warsaw, July 1995. As a
new result, we show that the space of finite type invariants of integral
homology 3-spheres is a graded polynomial algebra generated by invariants
additive under the connected sum. We also discuss some open questions on this
subject.Comment: 27 pages, amslatex. A new section was added surveying recent
developments of the subject. To appear in the proceedings of Warsaw knot
theory workshop, July-August 199
A volume-ish theorem for the Jones polynomial of alternating knots
The Volume conjecture claims that the hyperbolic Volume of a knot is
determined by the colored Jones polynomial.
The purpose of this article is to show a Volume-ish theorem for alternating
knots in terms of the Jones polynomial, rather than the colored Jones
polynomial: The ratio of the Volume and certain sums of coefficients of the
Jones polynomial is bounded from above and from below by constants.
Furthermore, we give experimental data on the relation of the growths of the
hyperbolic volume and the coefficients of the Jones polynomial, both for
alternating and non-alternating knots.Comment: 14 page
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