Construction and properties of the t-invariant
S. V. Matveev, M. A. Ovchinnikov, M. V. Sokolov
Abstract
We define a 3-manifold invariant t(M)=a+bg,
where a, b are integers and g
is a root of g^2-g-1. An advantage of the invariant is that it admits
a very simple fake surface interpretation and a simple self-contained proof
of the invariance. Actually it coincides with the homologically trivial part of
Turaev-Viro invariant of degree r=5. We give a simple formula for
calculation of the t-invariant
on lens spaces. Extensive tables relative to all closed irreducible
orientable 3-manifolds of complexity <7 are explicitly presented.
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