Euclidean Simplices and Invariants of Three-manifolds: a Modification of the Invariant for Lens Spaces

It is well-known that any two triangulations of a piecewise-linear three-manifold can be transformed into each other using local “Pachner moves”. If we construct an algebraic expression depending on some values ascribed to a manifold triangulation and invariant under these moves, we get a value that does not depend on a specific triangulation. It is natural to call such value an invariant of the manifold. The paper is organized as follows. In section 2 we repeat some arguments and constructions from papers [1], [2] and [3]. We use the universal cover of the manifold from the very beginning, and this leads us to a nontrivial modification of the invariant from paper [1]. In section 3 we calculate our modified invariant for lens spaces L(p, q) and do some remarks about its possible relationship with the Reidemeister torsion.