Geometry & Topology 7 (2003) 773–787

DOI: 10.2140/gt.2003.7.773

arXiv: math.GT/0301041

Abstract

Given an oriented rational homology 3–sphere M, it is known how to associate to any Spin^c–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 Spin^c–structures on M: Turaev's charges vs Chern vectors.

Keywords

rational homology 3–sphere, Reidemeister torsion, complex spin structure, quadratic function

Mathematical Subject Classification

Primary: 57M27

Secondary: 57Q10, 57R15

References

Forward citations

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