Cohomology of groups of diffeomorphisms related to the modules of differential operators on a smooth manifold

Research output: Contribution to journalArticle

Abstract

Let M be a manifold and T * M be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of M with values in the space of linear differential operators acting on C (T * M). When M is the n-dimensional sphere, S n, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of S n, with coefficients in the space of linear differential operators acting on contravariant tensor fields.

Original languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalJournal of Nonlinear Mathematical Physics
Volume9
Issue number4
DOIs
StatePublished - Jan 1 2002

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Group of Diffeomorphisms
Cohomology of Groups
Linear Differential Operator
differential operators
Smooth Manifold
homology
Cocycle
Differential operator
Contravariant tensor
modules
Module
Cotangent Bundle
n-dimensional
bundles
Coefficient
tensors
coefficients

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "Let M be a manifold and T * M be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of M with values in the space of linear differential operators acting on C ∞(T * M). When M is the n-dimensional sphere, S n, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of S n, with coefficients in the space of linear differential operators acting on contravariant tensor fields.",
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