| Abstract: | In 1991, Turaev and Viro constructed a quantum topological linear representation of mapping class groups of closed surfaces.
To the mappings of a surface into itself, they assigned simple polyhedra whose boundaries consisted of two simple graphs cutting
the surface into cells. The computational complexity of the Turaev-Viro representations strongly depends on the choice of
suitable sets of simple polyhedra. In this paper, simple polyhedra for the torus are constructed. One of the reasons why they
are convenient is that they all are obtained by gluing along boundary of copies of the same simple polyhedron.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 533–539, October, 1999. |
