Geodesic
Construction and properties of the $t$-invariant
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 207-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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The $t$-invariant is a new invariant of a compact 3-manifold. We construct this invariant by means of special spine theory. Behavior of the $t$-invariant under connected sum and under boundary connected sum is described. One of the Turaev–Viro invariants is expressed through the $t$-invariant. We show that the $t$-invariant fits into the conception of TQFT. We present the values of the $t$-invariant for all closed irreducible orientable 3-manifolds of complexity $\le6$, and for all lens spaces. Also some upper estimate for the number of values of the $t$-invariant of a Seifert manifold over a given closed surface with $n$ exceptional fibers is obtained. 
@article{ZNSL_2000_267_a14,
     author = {S. V. Matveev and M. A. Ovchinnikov and M. V. Sokolov},
     title = {Construction and properties of the $t$-invariant},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--219},
     year = {2000},
     volume = {267},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a14/}
}
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S. V. Matveev; M. A. Ovchinnikov; M. V. Sokolov. Construction and properties of the $t$-invariant. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 207-219. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a14/