Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-22T20:10:48.840Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 November 2018

M. V. Sokolov
M. V. Sokolov*
Affiliation:
Department of Mathematics, Chelyabinsk State University, Ul. Br. Kashirinykh 129 454136, ChelyabinskRussia, e-mail: sok@cgu.chel.su
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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. Tables of the invariants for closed orientable 3-manifolds of complexity ≤ 3 are presented at the end of the paper.

Keywords

57N1057M20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 468 - 475
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Casier, B. G., An imbedding for connected 3-manifolds with boundary, Proc. Amer. Math. Soc. 16(1965), 559–566.Google Scholar
2. Kauffman, L. H., Lins, S., Computing Turaev-Viro invariants for 3-manifolds, Manuscripta Math. 72(1991), 81–94.Google Scholar
3. Matveev, S. V., Complexity theory of three-dimensional manifolds, Acta Applicandae Mathematical 19 (1990), 101–130.Google Scholar
4. Matveev, S. V., Transformations of special spines and the Zeeman conjecture, Math. USSR Izvestia, 31 (1988), 423–434.Google Scholar
5. Piergallini, R., Standard moves for standard poly hedra and spines, Rend. Circ. Mat. Palermo, 37, 18(1988), 391–414.Google Scholar
6. Sokolov, M. V., On Turaev-Viro invariants for 3-manifolds, VINITI preprint 583-B 93 (Russian).Google Scholar
7. Turaev, V. G., Viro, O. Y., State sum invariants of 3-manifolds and quantum 6j-symbols, Topology, 31(1992), 865–902.Google Scholar