Related papers: Analytic Torsion on Manifolds with Edges

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background…

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 prove the equality of the analytic torsion and the value at zero of a Ruelle dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold. This solves a conjecture of…

We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the…

We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our…

In this paper we study the analytic torsion for a complete oriented hyperbolic manifold of finite volume. This requires the definition of a regularized trace of heat operators. We use the Selberg trace formula to study the asymptotic…

In this paper we study the asymptotic behavior (in the sense of meromorphic functions) of the zeta function of a Laplace-type operator on a closed manifold when the underlying manifold is stretched in the direction normal to a dividing…

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 $G$ be a finitely generated torsion-free nilpotent group. The representation zeta function $\zeta_G(s)$ of $G$ enumerates twist isoclasses of finite-dimensional irreducible complex representations of $G$. We prove that $\zeta_G(s)$ has…

For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of SL_2(C) to the corresponding…

In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the…

We explicitly write down all eigenvalues of the Rumin Laplacian on the standard contact spheres, and express the analytic torsion functions associated with the {Rumin complex} in terms of the Riemann zeta function. In particular, we find…

For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems we define the Reidemeister torsion of the Borel-Serre compactification of the manifold using bases of cohomology classes defined via…

For a differentiable manifold $M$, a pair $(M, \nabla)$ is called an affine manifold if $\nabla$ is a flat and torsion-free connection on the tangent bundle $TM\rightarrow M$. A Riemannian metric $g$ on $M$ is said to be a Hessian metric on…

We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…

We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as $\phi$-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing…

The holomorphic torsion of a compact locally symmetric manifold is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.

We study the analytic torsion of odd-dimensional hyperbolic orbifolds $\Gamma \backslash \mathbb{H}^{2n+1}$, depending on a representation of $\Gamma$. Our main goal is to understand the asymptotic behavior of the analytic torsion with…

The formula for analytic torsion of a cone in even dimensions is comprised of three terms. The first two terms are well understood and given by an algebraic combination of the Betti numbers and the analytic torsion of the cone base. 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…