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Spring 2010 Twisted Poincaré lemma and twisted Čech–de Rham isomorphism in case dimension =1
Ko-Ki Ito
Kyoto J. Math. 50(1): 193-204 (Spring 2010). DOI: 10.1215/0023608X-2009-009

Abstract

For a compact Riemann surface, (n+1)-tuple x:=(x0,,xn) of points on it, and a holomorphic vector bundle with an integrable connection on the open Riemann surface Xx deprived of (n+1) points x0,,xn, let L be the local system of horizontal sections of the connection. In this article, we give a suitable covering of Xx to calculate the Čech cohomology and describe the isomorphism between the cohomology and the twisted de Rham cohomology, which is the cohomology of the complex with the differentials given by the connection. This isomorphism is given by the integrations over Aomoto’s regularized paths, the so-called Euler type integrals.

For the family {Xx}x parametrized by x, we give a variant of the isomorphism.

Citation

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Ko-Ki Ito. "Twisted Poincaré lemma and twisted Čech–de Rham isomorphism in case dimension =1." Kyoto J. Math. 50 (1) 193 - 204, Spring 2010. https://doi.org/10.1215/0023608X-2009-009

Information

Published: Spring 2010
First available in Project Euclid: 13 April 2010

zbMATH: 1188.30050
MathSciNet: MR2629647
Digital Object Identifier: 10.1215/0023608X-2009-009

Subjects:
Primary: 33C60 , 33C70 , 55N05 , 58A12

Rights: Copyright © 2010 Kyoto University

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Vol.50 • No. 1 • Spring 2010
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