Noncommutative topology and the world's simplest index theorem

Details Noncommutative topology and the world's simplest index theorem Noncommutative topology and the world's simplest index theorem

2010-01-29

arxiv.org/abs/1001.5299v2

Proceedings of the National Academy of Sciences 107 (2010), no. 19, 8549-8556

Mathematics

Differential Geometry

17 pages; constants in Theorem 1 corrected; accepted for publication in Proc. Nat. Acad. Sci.

Scientific paper

This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how this theorem is a special case of a much more general index theorem for subelliptic operators on contact manifolds. Finally we discuss the noncommutative topology that is employed in the proof of this theorem. We present these results as an instance in which noncommutative topology is fruitful in proving a very explicit (analytic/geometric) classical result.

Affiliated with

Also associated with

No associations

Rating

Noncommutative topology and the world's simplest index 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 Noncommutative topology and the world's simplest index theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative topology and the world's simplest index theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-251747