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.
The Mayer-Vietoris Sequence for the Analytic Structure Group
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abstract
We develop a Mayer-Vietoris sequence for the analytic structure group explored by Higson and Roe. Using explicit formulas for Mayer-Vietoris boundary maps, we give a new proof and generalizations of Roe's partitioned manifold index theorem.
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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.