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Weak congruence and the quantum ideal of a 3-manifold
by
Patrick Gilmer
Louisiana State University
Fix an odd prime p. Let Ap denote a primitive 2pth root of unity and h = 1+Ap. Let Op denote Z[Ap]. The quantum ideal Jp(M) is the Op-ideal generated by the Ip-invariant of all links in a closed 3-manifold M. Then there is a non-negative integer ap(M) such that Jp(M) = (h)ap(M). ap is an invariant of weak p-congruence. Let c(M), cp(M), g(M) denote respectively the co-rank of π1(M), the p-cut number, and the Heegaard genus of M. Then c(m) ≤ cp(M) ≤ 2 ap(M)/(p-3) ≤ g(M).
Date received: April 1, 2008
Copyright © 2008 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 # cawt-24.