Document Type
Article
Publication Date
5-11-2010
Publication Title
Proceedings of the National Academy of Sciences of the United States of America
Department
Department of Mathematics
Abstract
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for 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 it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry.
DOI
10.1073/pnas.1003155107
Original Citation
van Erp E. Noncommutative topology and the world's simplest index theorem. Proc Natl Acad Sci U S A. 2010 May 11;107(19):8549-56. doi: 10.1073/pnas.1003155107. Epub 2010 Apr 23. PMID: 20418506; PMCID: PMC2889318.
Dartmouth Digital Commons Citation
van Erp, Erik, "Noncommutative Topology and the World’s Simplest Index Theorem" (2010). Dartmouth Scholarship. 1494.
https://digitalcommons.dartmouth.edu/facoa/1494
