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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Reidemeister–Turaev torsion modulo one of rational homology three-spheres

Florian Deloup and Gwenael Massuyeau

Geometry & Topology 7 (2003) 773–787

arXiv: math.GT/0301041

Abstract

Given an oriented rational homology 3–sphere M, it is known how to associate to any Spinc–structure σ 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,σ), 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 Spinc–structures on M: Turaev’s charges vs Chern vectors.

Keywords
rational homology $3$–sphere, Reidemeister torsion, complex spin structure, quadratic function
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57Q10, 57R15
References
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Publication
Received: 1 January 2003
Revised: 3 October 2003
Accepted: 7 November 2003
Published: 13 November 2003
Proposed: Robion Kirby
Seconded: Walter Neumann, Cameron Gordon
Authors
Florian Deloup
Laboratoire Emile Picard
UMR 5580 CNRS/Univ. Paul Sabatier
118 route de Narbonne
31062 Toulouse Cedex 04
France
Gwenael Massuyeau
Laboratoire Jean Leray
UMR 6629 CNRS/Univ. de Nantes
2 Rue de la Houssinière
BP 92208
44322 Nantes Cedex 03
France