摘要
We introduce a notion of cobordism of Callias-type operators overcomplete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application, we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a sum of indexes of Callias-type operators on two noncompact but topologically simpler manifolds. As another application, we give a new proof of the relative index theorem for Callias-type operators, which also leads to a new proof of the Callias index theorem.
源语言 | 英语 |
---|---|
页(从-至) | 1183-1203 |
页数 | 21 |
期刊 | Communications in Partial Differential Equations |
卷 | 41 |
期 | 8 |
DOI | |
出版状态 | 已出版 - 2 8月 2016 |
已对外发布 | 是 |
指纹
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Braverman, M., & Shi, P. (2016). Cobordism invariance of the index of Callias-type operators. Communications in Partial Differential Equations, 41(8), 1183-1203. https://doi.org/10.1080/03605302.2016.1183214