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arXiv · 1907.05578

Fibered Cusp b-Pseudodifferential Operators and its Applications

Jun Watanabe
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Abstract

Let $X$ be a smooth compact manifold with corners which has two embedded boundary hypersurfaces $\partial_0 X , \partial_1 X$, and a fiber bundle $\phi:\partial_0 X \to Y$ is given. By using the method of blowing up, we define a pseudodifferential culculus $\Psi ^* _{\Phi,b} (X)$ generalizing the $\Phi$-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" $\mathbb{Z}/k$ - manifolds is proved.

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Jun Watanabe. 2019-07-12. Fibered Cusp b-Pseudodifferential Operators and its Applications. https://arxiv.org/abs/1907.05578

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