Year: 2025
Type: preprint
Abstract: Roe's partitioned manifold index theorem applies when a complete Riemannian manifold $M$ is cut into two pieces along a compact hypersurface $N$. It states that a version of the index of a Dirac operator on $M$ localized to $N$ equals the index of the corresponding Dirac operator on $N$. This yields obstructions to positive scalar curvature, and implies cobordism invariance of the index of Dirac operators on compact manifolds. We generalize this result to cases where $N$ may be noncompact, under assumptions on the way it is embedded into $M$. This results in an equality between two classes in the $K$-theory of the Roe algebra of $N$. Bunke and Ludewig, and Engel and Wulff, have recently obtained related results based on different approaches.
Source: arXiv (Cornell University)
Authors: Hochs, Peter, de Kok, Thijs
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417440169
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