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=S³_K obtained by surgery around a knot K in cyclotomic form, we obtain a bound on the growth of the coefficients l_n(M) of hⁿ in Z_¥(S³_K), when considered as a formal power series in h=q-1.

This is consistent with the slope conjecture of Jacoby and Lawrence, namely that [(l_n(M))/(l_n-1(M))] is asymptotically linear in n with slope s(M). The bound obtained on s(S³_K) is of order the square of the number of crossings in K.

Date received: February 2, 2005