Index theorems for uniformly elliptic operators
Differential Geometry
2018-06-07 v1 K-Theory and Homology
Abstract
We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. The generalization will follow from a local index theorem that is valid on any manifold of bounded geometry. This local formula incorporates the uniform estimates present in the definition of uniform pseudodifferential operators.
Cite
@article{arxiv.1806.02035,
title = {Index theorems for uniformly elliptic operators},
author = {Alexander Engel},
journal= {arXiv preprint arXiv:1806.02035},
year = {2018}
}
Comments
Consists mostly of Section 5 of the preprint arXiv:1502.00494 which is being split up for easier publication. The latter arose out of the Ph.D. thesis arXiv:1410.8030 of the author. To appear in New York J. Math