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On a simple invariant of Turaev-Viro type. (English. Russian original) Zbl 0978.57008

J. Math. Sci., New York 94, No. 2, 1226-1229 (1999); translation from Zap. Nauchn. Semin. POMI 234, 137-142 (1996).
Summary: For 3-manifolds, we define an invariant \(t(M)=a+b \varepsilon\), where \(a,b\) are integers and \(\varepsilon=(1\pm\sqrt 5)2\). An advantage of the invariant is that it admits a very simple interpretation in terms of a fake surface and a simple geometric proof of the invariance. Actually, it coincides with the homologically trivial part of the Turaev-Viro invariant of degree \(r=5\). Extensive tables for all closed irreducible orientable 3-manifolds of complexity less than or equal to six are explicitly presented. Similar tables for \(r=3,4\) were composed by L. H. Kauffman and S. Lins [Manuscr. Math. 72, No. 1, 81-94 (1991; Zbl 0725.57008)].

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)

Citations:

Zbl 0725.57008
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