SL(2)-solution of the pentagon equation and invariants of three-dimensional manifolds

Details SL(2)-solution of the pentagon equation and invariants of three-dimensional manifolds SL(2)-solution of the pentagon equation and invariants of three-dimensional manifolds

2003-04-11

arxiv.org/abs/math/0304149v1

Theor. Math. Phys. 138, no. 1 (2004) 18--27

Mathematics

Algebraic Topology

13 pages; accepted for publication in Theor. Math. Phys

Scientific paper

10.1023/B:TAMP.0000010629.96356.

Building on a classical solution to the pentagon equation, constructed earlier by the author and E.V. Martyushev and related to the flat geometry invariant under the group SL(2), we construct an algebraic complex corresponding to a triangulation of a three-manifold. In case if this complex is acyclic (which is confirmed by examples), we use it for constructing a manifold invariant .

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