Invariant Summands of Turaev-Viro Invariants.
By Maxim Sokolov
Kandidatskaya Degree Dissertation Thesis. Thesis Advisor Prof. S. V. Matveev
I had planed to defend this
thesis in Fall'96, but in the spring I received an acceptance letter from
the George Washington University and decided to continue my education there,
postponing defending the dissertation in Russia. Therefore, by now this
dissertation thesis is not defended and I do not know whether it will be
defended in the future.
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to see this work get the self-extracting archive disser.exe
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Contents
Introduction
Chapter 1. Turaev-Viro invariant as sum of three invariants.
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Simple and special polyhedra and their transformations.
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Turaev-Viro invariants.
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Summand-invariants.
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Summand-invariants and triangulation.
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Values of summand-invariants.
Chapter 2. Invariant TV_0 and SO(3)-invariant.
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Kauffman bracket for even-colored graphs.
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SO(3)-invariant.
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Calculation TV_0-invariant using Kauffman bracket.
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Connection between TV_0-invariant and SO(3)-invariant.
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Kirby-Melvin formula (in case of Turaev-Viro invariants).
Chapter 3. Bi-color and Tri-color invariants of Turaev-Viro type,
Kauffman-Lins conjecture, t-invariant.
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Kauffman-Lins conjecture.
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Bi-color Turaev-Viro type invariants.
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t-invariants.
Chapter 4. Which lens spaces are distinguished by Turaev-Viro
Invariants.
Appendix. Values of Summand-Invariants for manifolds of complexity
at most 7.
Reference.
Intersections with published works.
Some chapters intersect with my published works
(or/and written in English works).
- Chapter 1 in the main part intersects with On
the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro
invariants.// Knot'95, Banach Center Publications 42, Warsaw, 1998, pp
310--321.
- No part of Chapter 2 is published anywhere.
- First section of Chapter 3 intersects with The
Turaev-Viro invariant is a sum of three invariants.// Canadian Math.
Bull., Vol. 39 (4), 1996, pp 468--475.
- Third section of Chapter 3 partially intersects with the paper S.
V. Matveev, M. A. Ovchinnikov, M. V. Sokolov.
Construction and properties of the t-invariant// Unpublished.
- Chapter 4 in the main part intersects with Which
lens spaces are distinguished by the Turaev-Viro invariants?// Mat.
Zametki, Vol. 61, No. 3 (1997), pp 468--470.
- English version of Appendix see in Tables.....
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