|
Organizers |
The slope conjecture for surgery around knots
by
Ruth Lawrence
Hebrew University, Jerusalem
Coauthors: Ofer Ron (Hebrew University)
Using Le and Habiro's techniques for computing the Ohtsuki invariant Z¥(M) of an integer homology 3-sphere M=S3K obtained by surgery around a knot K in cyclotomic form, we obtain a bound on the growth of the coefficients λn(M) of hn in Z¥(S3K), when considered as a formal power series in h=q−1.
This is consistent with the slope conjecture of Jacoby and Lawrence, namely that [(λn(M))/(λn−1(M))] is asymptotically linear in n with slope σ(M). The bound obtained on σ(S3K) is of order the square of the number of crossings in K.
Date received: February 2, 2005
Copyright © 2005 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capo-10.