This article is cited in 6 papers

$SL(2)$-Solution of the Pentagon Equation and Invariants of Three-Dimensional Manifolds

I. G. Korepanov

South Ural State University

Abstract: 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, acyclic complexes, torsion, invariants of manifolds.

Received: 23.12.2002

DOI: 10.4213/tmf11

 English version: Theoretical and Mathematical Physics, 2004, 138:1, 18–27

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