49 citations · 216 across the 41 of their papers we have counts for
12 papers · 1 filter
Virtually small spectral package of a Riemannian manifold
Dan Burghelea, Yoonweon Lee
For a Morse function on a closed orientable Riemannian manifold one introduces the {\it virtually small spectral package} an analytic object consisting of a finite number of analyt…
Witten deformation and the spectral package of a Riemannian manifold
Dan Burghelea
The Witten deformation associated to a Morse function on a closed Riemannian manifold, via Rellich-Kato theorem, relates analytically the spectral package of the Riemannian manifol…
Complex valued Ray--Singer torsion II
Dan Burghelea, Stefan Haller
In this paper we extend Witten-Helffer-Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-…
Complex valued Ray-Singer torsion
Dan Burghelea, Stefan Haller
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 topo…
Dynamics, Laplace transform and Spectral geometry
Dan Burghelea, Stefan Haller
We consider a vector field on a closed manifold which admits a Lyapunov one form. We assume has Morse type zeros, satisfies the Morse--Smale transversality condition and ha…
Torsion, as a function on the space of representations
Dan Burghelea, Stefan Haller
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…
Laplace transform, dynamics and spectral geometry
Dan Burghelea, Stefan Haller
We consider vector fields on a closed manifold with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class $ξ\in…
Euler structures, the variety of representations and the Milnor-Turaev torsion
Dan Burghelea, Stefan Haller
In this paper we extend and Poincare dualize the concept of Euler structures, introduced by Turaev for manifolds with vanishing Euler-Poincare characteristic, to arbitrary manifold…
A short course on Witten Helffer-Sjöstrand theory
Dan Burghelea
Witten-Helffer-Sjöstrand theory is an addition to Morse theory and Hodge-de Rham theory for Riemannian manifolds and considerably improves on them by injecting some spectral theory…
On the topology and analysis of a closed one form. I (Novikov's theory revisited)
Dan Burghelea, Stefan Haller
We consider systems with a closed smooth manifold, a real valued closed one form and a Riemannian metric, so that is a Morse-Smale pair, Definition~2.…
Lectures on Witten Helffer Sjöstrand Theory
Dan Burghelea
Witten- Helffer-Sjöstrand theory is a considerable addition to the De Rham- Hodge theory for Riemannian manifolds and can serve as a general tool to prove results about comparison…
Removing Metric Anomalies from Ray Singer Torsion
Dan Burghelea
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…