Related papers: Refined analytic torsion as analytic function on t…

We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…

We propose a definition for analytic torsion of the Rumin complex on contact manifolds. This is given by the derivative at zero of a well-chosen combination of zeta functions of a fourth-order modified Rumin Laplacian. The regular value at…

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…

Let X be a closed Riemannian manifold and let H\hookrightarrow X be an embedded hypersurface. Let X=X_+ \cup_H X_- be a decomposition of X into two manifolds with boundary, with X_+ \cap X_- = H. In this expository article, surgery -- or…

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 construct the analogue of Dedekind eta function for odd dimensional CY manifolds. We use the theory of determinant line bundles. We constructed a canonical holomorphic section $\eta^{N}$ of some power of the determinant…

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…

For a closed manifold equipped with a Riemannian metric, a triangulation, a representation of its fundamental group on an Hilbert module of finite type (over of finite von Neumann algebra), and a Hermitian structure on the flat bundle…

We prove that every smooth CR manifold $M\subset\subset \C^n$, of hypersurface type, has a complex strip-manifold extension in $\C^n$. If $M$ is, in addition, pseudoconvex-oriented, it is the "exterior" boundary of the strip. In turn, the…

We study eta-invariants on odd dimensional manifolds with boundary. The dependence on boundary conditions is best summarized by viewing the (exponentiated) eta-invariant as an element of the (inverse) determinant line of the boundary. We…

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…

The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of…

We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a…

In this paper we define a Poincar\'e-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial "torsion-type" invariant which…

We characterize the global maximizers of a certain non-local functional defined on the space of all positively curved metrics on an ample line bundle L over a Kahler manifold X. This functional is an adjoint version, introduced by…

I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms. The category of affine manifolds embeds as a…

This paper presents a perturbation analysis framework for nonsmooth optimization on connected Riemannian manifolds to bridge the gap between the rapid development of algorithmic approaches and a robust theoretical foundation. Using…

In this paper we study the asymptotic behavior of the analytic torsion for compact, oriented hyperbolic manifolds with respect to certain rays of representations obtained by restriction of irreducible representations of the group of…

The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained…

The purpose of this article is to study the asymptotic expansion of Ray-Singer analytic tosion associated with increasing powers p of a given positive line bundle. Here we prove that the asymptotic expansion associated to a manifold…