On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant
Abstract
Description
The Turaev-Viro invariant is defined as a certain state sum calculated on an arbitrary simple spine of a 3-manifold. We specify each term of the sum as 0-term, 1-term or 2-term such that each sum of the terms having the same type is an invariant too. The sum of the 0-terms is equal to the square of the modulus of the so-called SO(3)-invariant. In the paper we express the sum of the 0-terms and 2-terms and the sum of the 1-terms via the Turaev-Viro invariants. Tables of values of the invariants are enclosed. The values are presented as polynomials on primitive roots of unity with integer coefficients.
Plain TeX, 12 pages, no figures. In this version we added a definition of the invariant TV_1 on a triangulation, Lemma 3 and Remark 5 in section 6, some remarks about the tables. We also corrected the definition of an odd edge in section 6
Plain TeX, 12 pages, no figures. In this version we added a definition of the invariant TV_1 on a triangulation, Lemma 3 and Remark 5 in section 6, some remarks about the tables. We also corrected the definition of an odd edge in section 6