Geometry & Topology, Vol. 7 (2003)
Paper no. 22, pages 773--787.
Reidemeister-Turaev torsion modulo one of rational homology three-spheres
Florian Deloup and Gwenael Massuyeau
Given an oriented rational homology 3-sphere M, it is known how to
associate to any Spin^c-structure \sigma on M two quadratic functions
over the linking pairing. One quadratic function is derived from the
reduction modulo 1 of the Reidemeister-Turaev torsion of (M,\sigma ),
while the other one can be defined using the intersection pairing of
an appropriate compact oriented 4-manifold with boundary M. In this
paper, using surgery presentations of the manifold M, we prove that
those two quadratic functions coincide. Our proof relies on the
comparison between two distinct combinatorial descriptions of
Spin^c-structures on M Turaev's charges vs Chern vectors.
Rational homology 3-sphere, Reidemeister torsion, complex spin structure, quadratic function
AMS subject classification.
Secondary: 57Q10, 57R15.
Submitted to GT on 1 January 2003.
(Revised 3 October 2003.)
Paper accepted 7 November 2003.
Paper published 13 November 2003.
Notes on file formats
Florian Deloup, Gwenael Massuyeau
Laboratoire Emile Picard, UMR 5580 CNRS/Univ. Paul Sabatier
118 route de Narbonne, 31062 Toulouse Cedex 04, France
Laboratoire Jean Leray, UMR 6629 CNRS/Univ. de Nantes
2 rue de la Houssiniere, BP 92208, 44322 Nantes Cedex 03, France
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