2015/12/12 by Maxim Braverman, Braverman, Maxim, Pengshuai Shi +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1512.03939
openalex publication_date 2015/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a notion of cobordism of Callias-type operators over complete 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 non-compact, 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.