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Title: On the rapid decay homology of F.Pham (New development of microlocal analysis and singular perturbation theory)
Authors: Matsubara-Heo, Saiei-Jaeyeong
Keywords: 18G35
32S22
rapid decay homology of F.Pham
rapid decay homology
irregular Aomoto-Gelfand Hypergeometric functions
Issue Date: Jun-2019
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu
Volume: B75
Start page: 1
End page: 17
Abstract: In [9], M. Hien introduced rapid decay homology group H_{*}^{rd}(U, (nabla, E)) associated to an irregular connection (nabla, E) on a smooth complex affine variety U , and showed that it is the dual group of the algebraic de Rham cohomology group H_{dR}^{*}(U, (nabla^{vee}, E^{vee})) . On the other hand, F. Pham has already introduced his version of rapid decay homology when (nabla, E) is the socalled elementary irregular connection ([20]) in [18]. In this report, we will state a comparison theorem of these homology groups and give an outline of its proof. This can be regarded as a homological counterpart of the result [20] of C. Sabbah. As an application, we construct a basis of some rapid decay homologies associated to a hyperplane arrangement and hypersphere arrangement of Schlöfli type.
Description: "New development of microlocal analysis and singular perturbation theory". October 3-7, 2016. edited by Naofumi Honda and Yasunori Okada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
Rights: © 2019 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
URI: http://hdl.handle.net/2433/244766
Appears in Collections:B75 New development of microlocal analysis and singular perturbation theory

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