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RESEARCH BLOG 6/25/03 Notes on Perelman's work are now available. Kleiner and Lott have

Summary: RESEARCH BLOG 6/25/03
Notes on Perelman's work are now available. Kleiner and Lott have
written up notes on Perelman's first paper. Perelman's papers omit
many computations and details, so hopefully their notes will make it
much easier to read. There is also a link to notes on Perelman's lectures
at Stonybrook by Christine Sormani, which should shed some light on
his program. I've added slides on my talk on conjectures on minimal
surfaces and Ricci flow, which was given at Caltech, UCSB, and the
Georgia topology conference.
A paper was posted generalizing the volume conjecture by Gukov.
This conjecture relate limits of colored Jones polynomials to the vol-
ume of Dehn fillings on a hyperbolic knot. In particular, the conjecture
would imply that the colored Jones polynomials completely determine
the A-polynomial of a hyperbolic knot. This seems to be related to work
of Gelca, Frohman, and Lofaro, who generalize the A-polynomial to a
non-commutative version, and implicitly conjecture that it determines
the colored Jones polynomials. I suppose one could conjecture that
the colored Jones polynomials also determine the non-commutative A-
polynomial. If one believes Gukov's conjecture for all knots (not just
hyperbolic), then it would seem that the generalization of the volume


Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago


Collections: Mathematics