Related papers: Anomaly formulas for the complex-valued analytic t…

Co-Euler structures were studied by Burghelea and Haller on closed manifolds as dual objects to Euler structures. We extend the notion of co-Euler structures to the situation of compact manifolds with boundary. As an application, by…

We introduce an intrinsic deformation of the algebra of smooth functions on a compact Riemannian manifold using only the Laplace spectral decomposition. The construction twists the canonical multiplication-projection channels by unimodular…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer…

We define analytic torsion for the twisted de Rham complex, consisting of the spaces of differential forms on a compact oriented Riemannian manifold X valued in a flat vector bundle E, with a differential given by a flat connection on E…

In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…

Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined…

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 oriented odd dimensional manifold. Further, we calculate the…

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…

The Ray-Singer analytic torsion is the zeta-function trace of a certain sum of logarithm operators on the de Rham complex. In this note we examine the residue analytic torsion, defined using the residue-trace instead of the spectral zeta…

In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without…

Consider a flat vector bundle F over compact Riemannian manifold M and let f be a self-indexing Morse function on M. Let g be a smooth Euclidean metric on F. Set g_t=exp(-2tf)g and let \rho(t) be the Ray-Singer analytic torsion of F…

Recently, Cappell and Miller extended the classical construction of the analytic torsion for de Rham complexes to coupling with an arbitrary flat bundle and the holomorphic torsion for $\bar{\partial}$-complexes to coupling with an…

We show Riemannian geometry could be studied by identifying the tangent bundle of a Riemannian manifold $\mathcal{M}$ with a subbundle of the trivial bundle $\mathcal{M} \times \mathcal{E}$, obtained by embedding $\mathcal{M}$…

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…

For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation.…

Given a number field $F$ with ring of integers $\mathcal{O}_{F}$, one can associate to any torsion free subgroup of $\operatorname{SL}(2,\mathcal{O}_{F})$ of finite index a complete Riemannian manifold of finite volume with fibered cusp…

We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear…

We introduce and study a canonical quadratic form, called the torsion quadratic form, of the determinant line of a flat vector bundle over a closed oriented odd-dimensional manifold. This quadratic form caries less information than the…

We study a variational problem on a smooth manifold with a decomposition of the tangent bundle into $k>2$ subbundles (distributions), namely, we consider the integrated sum of their mixed scalar curvatures as a functional of adapted…