We define analytic torsion $\tau (X,\mathcal {E}, H)\in\operatorname {det}
H^{\bullet}(X,\mathcal {E}, H) $ for the twisted de Rham complex, consisting of the spaces of …

We propose an analytic torsion for the Rumin complex associated with generic rank two
distributions on closed 5-manifolds. This torsion behaves as expected with respect to …

We introduce a new object, the dynamical torsion, which extends the potentially ill-defined
value at $0 $ of the Ruelle zeta function of a contact Anosov flow twisted by an acyclic …

The work of Ray and Singer that introduced analytic torsion, a kind of determinant of the
Laplacian operator in topological and holomorphic settings, is naturally generalized in both …

In this paper we extend and Poincaré dualize the concept of Euler structures, introduced by
Turaev for manifolds with vanishing Euler–Poincaré characteristic, to arbitrary manifolds. We …

Abstract Riemannian Geometry, Topology and Dynamics permit to introduce partially
defined holomorphic functions on the variety of representations of the fundamental group of …

We show that the Ruelle dynamical zeta function on a closed odd dimensional locally
symmetric space twisted by an arbitrary flat vector bundle has a meromorphic extension to …

In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based
on fiber wise Hermitian metrics to nonselfadjoint Laplacians based on fiber wise non …

We show that the refined analytic torsion is a holomorphic section of the determinant line
bundle over the space of complex representations of the fundamental group of a closed …

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 …