New York Journal of Mathematics
Volume 24 (2018), 543-587


Alexander Engel

Index theorems for uniformly elliptic operators

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Published: August 25,2018.
Keywords: Index theory, pseudodifferential operators, uniform K-homology.
Subject: Primary: 58J20; Secondary: 19K56,47G30.

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.


This article arose out of the Ph.D.thesis of the author written at the University of Augsburg.

Author information

Alexander Engel:
Fakultät f&uamlr Mathematik, Universität Regensburg, D-93040 Regensburg, Germany