Flat vector bundles and analytic torsion forms
Xiaonan Ma (2000-2001)
Séminaire de théorie spectrale et géométrie
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Xiaonan Ma (2000-2001)
Séminaire de théorie spectrale et géométrie
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Diego Conti, Thomas Bruun Madsen (2015)
Complex Manifolds
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We introduce and study a notion of invariant intrinsic torsion geometrywhich appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S3. This space is foliated by sixdimensional hypersurfaces, each of which carries a particular type of SO(3)-structure; the intrinsic torsion is invariant under SO(3). The last condition is sufficient to imply local homogeneity of such geometries, and this allows us to give a classification. We close the circle by showing...
Jean-Michel Bismut (1990)
Mathematische Annalen
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Kai Köhler, Damien Roessler (2002)
Annales de l’institut Fourier
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This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.
Xiaonan Ma (2000)
Annales de l'institut Fourier
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In this paper, we calculate the behaviour of the equivariant Quillen metric by submersions. We thus extend a formula of Berthomieu-Bismut to the equivariant case.
Maxim Braverman, Thomas Kappeler (2007)
Annales de l’institut Fourier
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The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form on the determinant line of the cohomology. Both 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 . As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture...