38,178 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
Integral geometry of plane curves and knot invariants
We study the integral expression of a knot invariant obtained as the second
coefficient in the perturbative expansion of Witten's Chern-Simons path
integral associated with a knot. One of the integrals involved turns out to be
a generalization of the classical Crofton integral on convex plane curves and
it is related with invariants of generic plane curves defined by Arnold
recently with deep motivations in symplectic and contact geometry. Quadratic
bounds on these plane curve invariants are derived using their relationship
with the knot invariant.Comment: 18 pages, amslatex, 8 figures not included (will send upon request
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