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Abelian analytic torsion and symplectic volume

B.D.K. McLellan (2015)

Archivum Mathematicum

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.

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 ± 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...

Elliptic operators and higher signatures

Eric Leichtnam, Paolo Piazza (2004)

Annales de l’institut Fourier

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.

On the Burns-Epstein invariants of spherical CR 3-manifolds

Khoi The Vu (2011)

Annales de l’institut Fourier

In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.

On the L p index of spin Dirac operators on conical manifolds

André Legrand, Sergiu Moroianu (2006)

Studia Mathematica

We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from L p ( Σ ⁺ ) to L q ( Σ ¯ ) with p,q > 1. When 1 + n/p - n/q > 0 we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at (n+1)/2 - n/q instead of 0 in the definition of the eta invariant. In particular we reprove Chou’s formula for the L² index. For 1 + n/p - n/q ≤ 0 the index formula contains an extra term related to the Calderón projector.

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