Two Representations of the Fundamental Group and Invariants of Lens Spaces
نویسنده
چکیده
Let us shortly remind the main constructions of works [1], [2], [4]. Let there be given the universal covering of an oriented three-dimensional manifold, considered as a simplicial complex, in which every simplex is mapped into the three-dimensional Euclidean space (so that the intersections of their images in R are possible). To each edge is assigned thus a Euclidean length, and each tetrahedron has a sign “plus” or “minus” depending on orientation of its image in R; the defect angle (minus algebraic sum of dihedral angles) at each edge is equal to zero modulo 2π. Then we consider infinitesimal translations of vertices of the complex which lead to infinitesimal changes of edge lengths, while these latter lead, in their turn, to the infinitesimal changes of defect angles. Thus, the following sequence of vector spaces arises:
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