On the Noncommutative Residue for Projective Pseudodifferential Operators

Details On the Noncommutative Residue for Projective Pseudodifferential Operators On the Noncommutative Residue for Projective Pseudodifferential Operators

2010-05-21

arxiv.org/abs/1005.3953v2

Mathematics

Differential Geometry

17 pages, LaTeX, this second version replaces the first which contains a gap in the proof of the even dimensional case

Scientific paper

A well known result on pseudodifferential operators states that the noncommutative residue (Wodzicki residue) of a pseudodifferential projection vanishes. This statement is non-local and implies the regularity of the eta invariant at zero of Dirac type operators. We prove that in a filtered algebra the value of a projection under any residual trace depends only on the principal part of the projection. This general, purely algebraic statement applied to the algebra of projective pseudodifferential operators implies that the noncommutative residue factors to a map from the twisted K-theory of the co-sphere bundle. We use arguments from twisted K-theory to show that this map vanishes, thus showing that the noncommutative residue of a projective pseudodifferential projection vanishes. This also gives a very short proof in the classical setting.

Affiliated with

Also associated with

No associations

Rating

On the Noncommutative Residue for Projective Pseudodifferential Operators 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 On the Noncommutative Residue for Projective Pseudodifferential Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Noncommutative Residue for Projective Pseudodifferential Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-339704