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

@article{Sokolov1996OnTA, title={On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant}, author={Maxim Sokolov}, journal={Banach Center Publications}, year={1996}, volume={42}, pages={395-408} }

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…

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## References

SHOWING 1-10 OF 23 REFERENCES

The Turaev-viro Invariant for 3-Manifolds is a Sum of Three Invariants

- MathematicsCanadian Mathematical Bulletin
- 1996

Abstract We show that every Turaev-Viro invariant for 3-manifolds is a sum of three new invariants and discuss their properties. We also find a solution of a conjecture of L. H. Kauffman and S. Lins.…

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds

- Mathematics
- 1994

This is a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the…

Computing Turaev-Viro invariants for 3-manifolds

- Mathematics
- 1991

We give a simple surface interpretation for each summand in the evaluation of Turaev-Viro invariants, for the case of small (up to eighth) roots of unity. From this interpretation follows an…

COMBINATORIAL CALCULATION OF THE VARIOUS NORMALIZATIONS OF THE WITTEN INVARIANTS FOR 3-MANIFOLDS

- Mathematics
- 1992

Polynomial formulae for the Witten invariant of 3-manifolds for manifolds which bound plumbed 4-manifolds are developed via the combinatorial approach of Lickorish. A number of tables of calculations…

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds

- Mathematics
- 1994

I used to keep the entire spin networks literature in a small folder on my shelf. The recent explosion of interest in the subject has made this impossible; more is probably now written every week…

Quantum Invariants of Knots and 3-Manifolds

- Physics
- 1994

This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of…

TRANSFORMATIONS OF SPECIAL SPINES AND THE ZEEMAN CONJECTURE

- Mathematics
- 1988

Two transformations, called elementary, are defined for special spines, and it is shown that any one special spine of a 3-manifold can be obtained from any other by a sequence of elementary…

Visual geometry and topology

- Art
- 1994

The principal aim of this book is to narrate, in an accessible and fairly visual language, some classical and modern achievements of geometry and topology in both intrinsic mathematical problems and applications to mathematical physics.

Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology

- 1992