Index theorems for uniformly elliptic operators

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.

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

References in corpus (2)

• Index theory of uniform pseudodifferential operators
• Indices of pseudodifferential operators on open manifolds

Cited by in corpus (3)

• Uniform Roe algebras of uniformly locally finite metric spaces are rigid
• Corona Rigidity
• Spectral $\zeta$-invariants lifted to coverings