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- W2279908092 abstract "We study differential operators on complete Riemannian manifolds which act on sections of a bundle of finite type modules over a von Neumann algebra with a trace. We prove a relative index and a Callias-type index theorems for von Neumann indexes of such operators. We apply these results to obtain a version of Atiyah's $L^2$-index theorem, which states that the index of a Callias-type operator on a non-compact manifold $M$ is equal to the $Gamma$-index of its lift to a Galois cover of $M$. We also prove the cobordism invariance of the index of Callias-type operators. In particular, we give a new proof of the cobordism invariance of the von Neumann index of operators on compact manifolds." @default.
- W2279908092 created "2016-06-24" @default.
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- W2279908092 date "2016-02-22" @default.
- W2279908092 modified "2023-09-27" @default.
- W2279908092 title "Callias-type operators in von Neumann algebras" @default.
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