A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem

Details A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem

2005-12-08

arxiv.org/abs/math/0512167v1

Advances in Mathematics, Volume 213, Issue 1, 1 August 2007, Pages 1-52

Mathematics

Differential Geometry

3 figures

Scientific paper

The Gauss-Bonnet Theorem is studied for edge metrics as a renormalized index theorem. These metrics include the Poincar\'e-Einstein metrics of the AdS/CFT correspondence. Renormalization is used to make sense of the curvature integral and the dimensions of the $L^2$-cohomology spaces as well as to carry out the heat equation proof of the index theorem. For conformally compact metrics even mod $x^m$, the finite time supertrace of the heat kernel on conformally compact manifolds is shown to renormalize independently of the choice of special boundary defining function.

Affiliated with

Also associated with

No associations

Rating

A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem 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 A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-443209