Distinguishing three-dimensional lens spaces L(7,1) and L(7,2) by means of classical pentagon equation

I. G. Korepanov; E. V. Martyushev

doi:10.2991/jnmp.2002.9.1.8

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Distinguishing three-dimensional lens spaces L(7,1) and L(7,2) by means of classical pentagon equation

I. G. Korepanov·E. V. Martyushev

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Abstract

We construct new topological invariants of three-dimensional manifolds which can, in particular, distinguish homotopy equivalent lens spaces L(7,1) and L(7,2). The invariants are built on the base of a classical (not quantum) solution of pentagon equation, i.e.algebraic relation corresponding to a ``2 tetrahedra to 3 tetrahedra'' local re-building of a manifold triangulation. This solution, found earlier by one of the authors, is expressed in terms of metric characteristics of Euclidean tetrahedra.

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I. G. Korepanov, E. V. Martyushev. 2002-10-22. Distinguishing three-dimensional lens spaces L(7,1) and L(7,2) by means of classical pentagon equation. https://doi.org/10.2991/jnmp.2002.9.1.8

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