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TitleIdeal Turaev–Viro invariants
Author(s) Simon A. King
TypeArticle in Journal
AbstractTuraev–Viro invariants are defined via state sum polynomials associated to a special spine or a triangulation of a compact 3-manifold. By evaluation of the state sum at any solution of the so-called Biedenharn–Elliott equations, one obtains a homeomorphism invariant of the manifold (“numerical Turaev–Viro invariant”). The Biedenharn–Elliott equations define a polynomial ideal. The key observation of this paper is that the coset of the state sum polynomial with respect to that ideal is a homeomorphism invariant of the manifold (“ideal Turaev–Viro invariant”), stronger than the numerical Turaev–Viro invariants. Using computer algebra, we obtain computational results on several examples of ideal Turaev–Viro invariants, for all closed orientable irreducible manifolds of complexity at most 9.
KeywordsTuraev–Viro invariant, Gröbner basis, Quantum invariant, Special spine
ISSN0166-8641
URL http://www.sciencedirect.com/science/article/pii/S0166864106003555
LanguageEnglish
JournalTopology and its Applications
Volume154
Number6
Pages1141 - 1156
Year2007
Edition0
Translation No
Refereed No
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