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2011•Bulletin of the Australian Mathematical SocietyOpen access

QUASIMODULAR FORMS AND COHOMOLOGY

Min Ho Lee

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Abstract

Abstract We construct linear maps from the spaces of quasimodular forms for a discrete subgroup Γ of SL(2,ℝ) to some cohomology spaces of the group Γ and prove that these maps are equivariant with respect to appropriate Hecke operator actions. The results are obtained by using the fact that there is a correspondence between quasimodular forms and certain finite sequences of modular forms.

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Abstract We construct linear maps from the spaces of quasimodular forms for a discrete subgroup Γ of SL(2,ℝ) to some cohomology spaces of the group Γ and prove that these maps are equivariant with respect to appropriate Hecke operator actions. The results are obtained by using the fact that there is a correspondence between quasimodular forms and certain finite sequences of modular forms.

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Available abstract

Abstract We construct linear maps from the spaces of quasimodular forms for a discrete subgroup Γ of SL(2,ℝ) to some cohomology spaces of the group Γ and prove that these maps are equivariant with respect to appropriate Hecke operator actions. The results are obtained by using the fact that there is a correspondence between quasimodular forms and certain finite sequences of modular forms.

Key concepts: Mathematics, Equivariant map, Pure mathematics, Cohomology, Equivariant cohomology, Modular form, Algebra over a field, Construct (python library)

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