On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant

Details On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant

1996-01-15

arxiv.org/abs/q-alg/9601013v2

Knot Theory, Banach Center Publ., Vol. 42, 1998, pp 395--408

Mathematics

Quantum Algebra

Plain TeX, 12 pages, no figures. In this version we added a definition of the invariant TV_1 on a triangulation, Lemma 3 and R

Scientific paper

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.

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