Displaying similar documents to “Local index theory and higher analytic torsion.”

Reidemeister Torsion and Analytic Torsion of Discs

T. de Melo, L. Hartmann, M. Spreafico (2009)

Bollettino dell'Unione Matematica Italiana

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We study the Reidemeister torsion and the analytic torsion of the m-dimensional disc in the Euclidean m-dimensional space, using the base for the homology defined by Ray and Singer in [10]. We prove that the Reidemeister torsion coincides with the square root of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Müller theorem. We use a formula proved by Brüning and Ma [1], that predicts a new...

Comparison of the refined analytic and the Burghelea-Haller torsions

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 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 ± 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...

The torsion theory and the Melkersson condition

Takeshi Yoshizawa (2020)

Czechoslovak Mathematical Journal

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We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson...

Abelian analytic torsion and symplectic volume

B.D.K. McLellan (2015)

Archivum Mathematicum

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This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.