Hecke operators on de Rham cohomology
type: Item
instance of: scholarly article
title: Hecke operators on de Rham cohomology
zbMATH Open document ID: 1054.58001
author: Min Ho Lee
published in: Revista Matemática Complutense
publication date: 2004-11-01T00:00:00Z
full work available at URL: https://eudml.org/doc/44521
review text: The author introduces the notion of Hecke operators on de Rham cohomology of a compact oriented manifolds. Such an operator is determined by a pair of covering maps of the given manifold. When the manifolds are regarded as quotients of their universal covering space by discrete subgroup of its group of diffeomorphisms, the properties of these operators are discussed. Automorphic forms on a Hermitian symmetric domain for a discrete subgroup of the corresponding semisimple Lie group as well as Hecke operators acting on the space of such automorphic forms are described. A correspondence between the space of modular forms of weight one and a subspace of the de Rham cohomology space is established. It is proved that the Hecke operators on modular forms are compatible with a special type of Hecke operators on de Rham cohomology under this correspondence.
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 58-06
Mathematics Subject Classification ID: 11F60
zbMATH DE Number: 2113558
zbMATH Keywords: Hecke operators on cohomology
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: compact oriented manifolds
zbMATH Keywords: automorphic forms
zbMATH Keywords: Hermitian symmetric domain
zbMATH Keywords: pair of covering maps
zbMATH Keywords: quotients of universal covering space
zbMATH Keywords: discrete subgroup of diffeomorphisms
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: space of modular forms of weight one
MaRDI profile type: Publication
DOI: 10.5209/REV_REMA.2004.V17.N1.16786
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description: scientific article; zbMATH DE number 2113558