Integral geometry of plane curves and knot invariants

Details Integral geometry of plane curves and knot invariants Integral geometry of plane curves and knot invariants

1994-11-30

arxiv.org/abs/dg-ga/9411015v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, amslatex, 8 figures not included (will send upon request)

Scientific paper

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.

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