2019/07/12 by Jun Watanabe, Watanabe, Jun
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1907.05578
openalex publication_date 2019/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth compact manifold with corners which has two embedded boundary hypersurfaces ∂0 X , ∂1 X, and a fiber bundle ϕ:∂0 X → Y is given. By using the method of blowing up, we define a pseudodifferential culculus Ψ^* Φ,b (X) generalizing the Φ-calculus of Mazzeo and Melrose and the (small) b-calculus of Melrose. We discuss the Fredholm condition of such operators and prove the relative index theorem. And as its application, the index theorem of "non-closed" ℤ/k - manifolds is proved.