Weak congruence and the quantum ideal of a 3-manifold
by
Patrick Gilmer
Louisiana State University

Fix an odd prime p. Let A_p denote a primitive 2pth root of unity and h = 1+A_p. Let O_p denote Z[A_p]. The quantum ideal J_p(M) is the O_p-ideal generated by the I_p-invariant of all links in a closed 3-manifold M. Then there is a non-negative integer a_p(M) such that J_p(M) = (h)^a_p(M). a_p is an invariant of weak p-congruence. Let c(M), c_p(M), g(M) denote respectively the co-rank of p₁(M), the p-cut number, and the Heegaard genus of M. Then c(m) ≤ c_p(M) ≤ 2 a_p(M)/(p-3) ≤ g(M).

Date received: April 1, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawt-24.