Existence of spectral gaps, covering manifolds and residually finite groups

Details Existence of spectral gaps, covering manifolds and residually finite groups Existence of spectral gaps, covering manifolds and residually finite groups

2005-03-03

arxiv.org/abs/math-ph/0503005v3

Physics

Mathematical Physics

final version (26 pages, 2 figures). to appear in Rev. Math. Phys

Scientific paper

In the present paper we consider Riemannian coverings $(X,g) \to (M,g)$ with residually finite covering group $\Gamma$ and compact base space $(M,g)$. In particular, we give two general procedures resulting in a family of deformed coverings $(X,g_\eps) \to (M,g_\eps)$ such that the spectrum of the Laplacian $\Delta_{(X_\eps,g_\eps)}$ has at least a prescribed finite number of spectral gaps provided $\eps$ is small enough. If $\Gamma$ has a positive Kadison constant, then we can apply results by Br\"uning and Sunada to deduce that $\spec \Delta_{(X,g_\eps)}$ has, in addition, band-structure and there is an asymptotic estimate for the number $N(\lambda)$ of components of $\spec {\laplacian {(X,g_\eps)}}$ that intersect the interval $[0,\lambda]$. We also present several classes of examples of residually finite groups that fit with our construction and study their interrelations. Finally, we mention several possible applications for our results.

Affiliated with

Also associated with

No associations

Rating

Existence of spectral gaps, covering manifolds and residually finite groups 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 Existence of spectral gaps, covering manifolds and residually finite groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence of spectral gaps, covering manifolds and residually finite groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-24299