Geodesic
$SL(2)$-Solution of the Pentagon Equation and Invariants of Three-Dimensional Manifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 1, pp. 23-34

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We construct an algebraic complex corresponding to a triangulation of a three-manifold starting with a classical solution of the pentagon equation, constructed earlier by the author and Martyushev and related to the flat geometry, which is invariant under the group $SL(2)$. If this complex is acyclic (which is confirmed by examples), we can use it to construct an invariant of the manifold.
Keywords: pentagon equation, Pachner moves, invariants of manifolds.
Mots-clés : acyclic complexes, torsion 
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     author = {I. G. Korepanov},
     title = {$SL(2)${-Solution} of the {Pentagon} {Equation} and {Invariants} of {Three-Dimensional} {Manifolds}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--34},
     publisher = {mathdoc},
     volume = {138},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_1_a1/}
}
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I. G. Korepanov. $SL(2)$-Solution of the Pentagon Equation and Invariants of Three-Dimensional Manifolds. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 1, pp. 23-34. http://geodesic.mathdoc.fr/item/TMF_2004_138_1_a1/