On a simple invariant of Turaev-Viro type

Abstract

For 3-manifolds, we define an invariant t(M)=a+be, 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.