The authors define a relative coarse index, prove it computes submanifold indices via a Thom class, and use it to build scalar curvature obstructions away from submanifolds.
Elliptic regularity for Dirac operators on families of noncompact manifolds
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abstract
We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.
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math.KT 1years
2025 1verdicts
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The relative index in coarse index theory and submanifold obstructions to uniform positive scalar curvature
The authors define a relative coarse index, prove it computes submanifold indices via a Thom class, and use it to build scalar curvature obstructions away from submanifolds.