On the absolute value of the SO(3)-invariant and other summands of
the Turaev-Viro invariant
M. V. Sokolov
Abstract
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.
This paper is available at the e-archives: http://xxx.lanl.gov/abs/q-alg/9601013
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