Abstract
For 3-manifolds, we define an invariant t(M)=a+bε, 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. Bibliography: 8 titles.
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References
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Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 137–142.
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Matveev, S.V., Sokolov, M.V. On a simple invariant of Turaev-Viro type. J Math Sci 94, 1226–1229 (1999). https://doi.org/10.1007/BF02364878
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DOI: https://doi.org/10.1007/BF02364878