Residues and Hyperfunctions

Tatsuo Suwa ()
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Tatsuo Suwa: Hokkaido University, Department of Mathematics

Chapter Chapter 8 in Handbook of Geometry and Topology of Singularities III, 2022, pp 565-644 from Springer

Abstract: Abstract We discuss relative Čech-de Rham and relative Čech-Dolbeault cohomologies and their applications. In the de Rham case, we are mainly concerned with the residues that arise from the localization of characteristic classes via the Alexander duality. The relative Čech-de Rham theorem allows us to deal with the problem from both the topological and differential geometric viewpoints and the comparison of the two yields various interesting expressions of the residues and applications. In the Dolbeault case, the relative Čech-Dolbeault cohomology turns out to be canonically isomorphic with the relative cohomology of the sheaf of holomorphic forms. As an application, we give explicit expressions of Sato hyperfunctions and related operations including the embedding of the space of real analytic functions into that of hyperfunctions, where as well the Thom class plays an important role.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-95760-5_8

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DOI: 10.1007/978-3-030-95760-5_8

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