Geodesic
On a~simple invariant of Turaev--Viro type
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 137-142

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We define a 3-manifold invariant $t(M)=a+b\varepsilon$, where $a,b$ are integers and $\varepsilon=(1\pm\sqrt5)/2$. 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. Bibl. 8 titles. 
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     author = {Sergei V. Matveev and Maxim V. Sokolov},
     title = {On a~simple invariant of {Turaev--Viro} type},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a9/}
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Sergei V. Matveev; Maxim V. Sokolov. On a~simple invariant of Turaev--Viro type. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 137-142. http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a9/