Related papers: Twisted Analytic Torsion and Adiabatic Limits
We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a…
Let $E$ be a flat complex vector bundle over a closed oriented odd dimensional manifold $M$ endowed with a flat connection $\nabla$. The refined analytic torsion for $(M,E)$ was defined and studied by Braverman and Kappeler. Recently Mathai…
We review the Reidemeister torsion, Ray-Singer's analytic torsion and the Cheeger-M"uller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties.…
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…
We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer…
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 extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a…
In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds and prove that they are metric independent.…
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…
In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each…
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.…
It is shown that for any piecewise-linear closed orientable manifold of odd dimension there exists an invariantly defined metric on the determinant line of cohomology with coefficients in an arbitrary flat bundle E over the manifold (E is…
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…
A linear or multi-linear valuation on a finite abstract simplicial complex can be expressed as an analytic index dim(ker(D)) -dim(ker(D^*)) of a differential complex D:E -> F. In the discrete, a complex D can be called elliptic if a…
The refined analytic torsion, defined by M. Braverman and T. Kappeler on closed manifolds, can be viewed as a refinement of the Ray-Singer torsion, since it is a canonical choice of an element with Ray-Singer norm one, in case of unitary…
We prove a formula relating the analytic torsion and Reidemeister torsion on manifolds with boundary in the general case when the metric is not necessarily a product near the boundary. The product case has been established by W. Lu\"ck and…
In this paper we study the analytic torsion of an odd-dimensional manifold with isolated conical singularities. First we show that the analytic torsion is invariant under deformations of the metric which are of higher order near the…
Torsion invariants for manifolds which are not simply connected were introduced by K. Reidemeister and generalized to higher dimensions by W. Franz. The Reidemeister torsion, was the first invariant of manifolds which was not a homotopy…
We prove that refined analytic torsion on a manifold with boundary is an analytic section of the determinant line bundle over the representation variety. As a fundamental application we establish a gluing formula for refined analytic…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…