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- W2735767807 abstract "We exhibit geometric situations, where higher indices of the spinor Dirac operator on a spin manifold $N$ are obstructions to positive scalar curvature on an ambient manifold $M$ that contains $N$ as a submanifold. In the main result of this note, we show that the Rosenberg index of $N$ is an obstruction to positive scalar curvature on $M$ if $N hookrightarrow M twoheadrightarrow B$ is a fiber bundle of spin manifolds with $B$ aspherical and $pi_1(B)$ of finite asymptotic dimension. The proof is based on a new variant of the multi-partitioned manifold index theorem which might be of independent interest. Moreover, we present an analogous statement for codimension one submanifolds. We also discuss some elementary obstructions using the $hat{A}$-genus of certain submanifolds." @default.
- W2735767807 created "2017-07-21" @default.
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- W2735767807 date "2017-09-19" @default.
- W2735767807 modified "2023-09-23" @default.
- W2735767807 title "An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds" @default.
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- W2735767807 doi "https://doi.org/10.2140/agt.2017.17.3081" @default.
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