Related papers: Ray-Singer Type Theorem for the Refined Analytic T…

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed aspherical manifold, we show that T gives…

Zero modes are an essential part of topological field theories, but they are frequently also an obstacle to the explicit evaluation of the associated path integrals. In order to address this issue in the case of Ray-Singer Torsion, which…

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…

We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the…

Ray Singer torsion is a numerical invariant associated with a compact Riemannian manifold equipped with a flat bundle and a Hermitian structure on this bundle. In this note we show how one can remove the dependence on the Riemannian metric…

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 study matrix models in the beta ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first beta-deformed corrections in the one-cut and the two-cut cases, as well as…

The universal invariant with respect to a given ribbon Hopf algebra is a tangle invariant that dominates all the Reshetikhin-Turaev invariants built from the representation theory of the algebra. We construct a canonical strict monoidal…

We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a…

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…

This paper is devoted to a proof of a generalized Ray-Singer conjecture for a manifold with boundary (the Dirichlet and the Neumann boundary conditions are independently given on each connected component of the boundary and the transmission…

A refined transfer is defined for the purpose of defining a refined version of the families torsion of Dwyer, Weiss, and Williams.

We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to…

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about…

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.…

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…

Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1|1) model of Rozansky and Saleur on $\Sigma x S^{1}$, both directly and using equivalent two-dimensional…

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…

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…

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the…