Some finiteness properties for the Reidemeister-Turaev torsion of three-manifolds

Mathematics – Geometric Topology

Scientific paper

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36 pages, 7 figures. Minor changes in this third and final version

Scientific paper

We prove for the Reidemeister-Turaev torsion of closed oriented three-manifolds some finiteness properties in the sense of Goussarov and Habiro, that is, with respect to some cut-and-paste operations which preserve the homology type of the manifolds. In general, those properties require the manifolds to come equipped with an Euler structure and a homological parametrization.

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