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arXiv · 2506.14301

The relative index in coarse index theory and submanifold obstructions to uniform positive scalar curvature

Alexander Engel·Christopher Wulff
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Abstract

We provide a coarse version of the relative index of Gromov and Lawson and thoroughly establish all of its basic properties. As an application, we discuss a general procedure to construct wrong way maps on the $K$-theory of the Roe algebra mapping the coarse index class of the Dirac operator of a manifold to the one of a suitably embedded submanifold of arbitrary codimension, thereby establishing an abstract machinery to find obstructions to uniform positive scalar curvature coming from these submanifolds.

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Alexander Engel, Christopher Wulff. 2025-06-17. The relative index in coarse index theory and submanifold obstructions to uniform positive scalar curvature. https://arxiv.org/abs/2506.14301

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