Mathematics – Analysis of PDEs
Scientific paper
2009-07-20
Mathematics
Analysis of PDEs
39 pages, 2 figures, LaTeX
Scientific paper
Scattering theory for p-forms on manifolds with cylindrical ends has a direct interpretation in terms of cohomology. Using the Hodge isomorphism,the scattering matrix at low energy may be regarded as operator on the cohomology of the boundary. Its value at zero describes the image of the absolute cohomology in the cohomology of the boundary. We show that the so-called scattering length, the Eisenbud-Wigner time delay at zero energy, has a cohomological interpretation as well. Namely, it relates the norm of a cohomology class on the boundary to the norm of its image under the connecting homomorphism in the long exact sequence in cohomology. An interesting consequence of this is that one can estimate the scattering lengths in terms of geometric data like the volumes of certain homological systoles.
Muller Werner
Strohmaier Alexander
No associations
LandOfFree
Scattering at low energies on manifolds with cylindrical ends and stable systoles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Scattering at low energies on manifolds with cylindrical ends and stable systoles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scattering at low energies on manifolds with cylindrical ends and stable systoles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-174697