Elliptic regularity for Dirac operators on families of noncompact manifolds

Abstract

We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^{\ast }$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.

Revised version. The title has been changed and many minor corrections have been done

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• The positive scalar curvature cobordism category
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• Coarse geometry and Callias quantisation
• Positive scalar curvature and an equivariant Callias-type index theorem for proper actions
• The Kasparov product on submersions of open manifolds
• An Obstruction to Higher-Dimensional Kernel of Dirac Operators