Related papers: Twisted Analytic Torsion and Adiabatic Limits

In the spirit of Ray and Singer we define a complex valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined…

For a closed, oriented, odd dimensional manifold $X$, we define the rho invariant $\rho(X,E,H)$ for the twisted odd signature operator valued in a flat hermitian vector bundle $E$, where $H = \sum i^{j+1} H_{2j+1}$ is an odd-degree closed…

We continue our investigations of the analytic properties of nonlinear twists of L-functions developed in [4],[5] and [7]. Given an L-function of degree d, we first extend the transformation formula in [5], relating a twist with leading…

The curvature of the noncommutative torus $T^2_\theta$ ($\theta$ irrational) endowed with a noncommutative conformal metric has been the focus of attention of several recent works. Continuing the approach taken in the paper [A. Connes and…

The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $\tau$ on the determinant line of the cohomology. Both $\tau$ and the Burghelea-Haller torsion are…

We introduce multi-torsion, a spectral invariant generalizing Ray-Singer analytic torsion. We define multi-torsion for compact manifolds with a certain local geometric product structure that gives a bigrading on differential forms. We prove…

In this paper we generalized the variational formulas for the determinants of the Laplacians on functions of CY metrics to forms of type (0,q) on CY manifolds. We also computed the Ray Singer Analytic torsion on CY manifolds we proved that…

In our earlier article [Lett. Math. Phys. 107 (2017), 475-503, arXiv:1409.8188], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every…

We study the analytic torsion of the cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the…

We construct an equivariant version of Ray-Singer analytic torsion for proper, isometric actions by locally compact groups on Riemannian manifolds, with compact quotients. We obtain results on convergence, metric independence, vanishing for…

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the…

The refined analytic torsion on compact Riemannian manifolds with boundary has been discussed by B. Vertman and the authors, but these two constructions are completely different. Vertman used a double of de Rham complex consisting of the…

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 \cite{RS}. We prove that the Reidemeister torsion…

We prove an analogue for odd dimensional manifolds with boundary, in the $b$-calculus setting, of the higher Atiyah-Patodi-Singer index theorem by Getzler and Wu, thus obtain a natural counterpart of the eta invariant for even dimensional…

We prove an extension of the Cheeger-M\"{u}ller theorem to spaces with isolated conical singularities: the $L^2$-analytic torsion coincides with the Ray-Singer intersection torsion on an even dimensional space, and they are trivial, while…

In this paper, we suggest a construction of determinant lines of finitely generated Hilbertian modules over finite von Neumann algebras. Nonzero elements of the determinant lines can be viewed as volume forms on the Hilbertian modules.…

The article consists of a survey on analytic and topological torsion. Analytic torsion is defined in terms of the spectrum of the analytic Laplace operator on a Riemannian manifold, whereas topological torsion is defined in terms of a…

Let (X,[\omega]) be a compact Kaehler manifold with a fixed Kaehler class [\omega]. Let K_\omega be the set of all Kaehler metrics on X whose Kaehler class equals [\omega]. In this paper we investigate the critical points of the functional…

In this paper, we study twisted arithmetic divisors on the modular curve X_0(N) with N square-free. For each pair (\Delta, r) where \Delta >0 and \Delta \equiv r^2 \mod 4N, we constructed a twisted arithmetic theta function \phi_{\Delta,…

We introduce the notion of a twisted differential operator of given radius relative to an endomorphism $$\sigma$$ of an affinoid algebra A. We show that this notion is essentially independent of the choice of the endomorphism $$\sigma$$. As…