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.
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Korepanov, I.G. SL(2)-Solution of the Pentagon Equation and Invariants of Three-Dimensional Manifolds. Theoretical and Mathematical Physics 138, 18–27 (2004). https://doi.org/10.1023/B:TAMP.0000010629.96356.52
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DOI: https://doi.org/10.1023/B:TAMP.0000010629.96356.52