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Comparison of the refined analytic and the Burghelea-Haller torsions

Maxim Braverman, Thomas Kappeler (2007)

Annales de l’institut Fourier

The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $τ$ on the determinant line of the cohomology. Both $τ$ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to $\pm τ$ . As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating...

Complex 2 Plane Bundles over CP(n).

Larry Smith (1978)

Manuscripta mathematica

Concordance and Bordism of Line Fields.

Ulrich Koschorke (1974)

Inventiones mathematicae

Connections and 1-jet fiber bundles

Pedro L. García (1972)

Rendiconti del Seminario Matematico della Università di Padova

Connections in regular Poisson manifolds over ℝ-Lie foliations

Jan Kubarski (2000)

Banach Center Publications

The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally,...