### 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 language | English (US) |
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Pages (from-to) | 455-463 |

Number of pages | 9 |

Journal | Journal of Nonlinear Mathematical Physics |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2002 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Cohomology of groups of diffeomorphisms related to the modules of differential operators on a smooth manifold.** / Bouarroudj, Sofiane.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Cohomology of groups of diffeomorphisms related to the modules of differential operators on a smooth manifold

AU - Bouarroudj, Sofiane

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036433671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036433671&partnerID=8YFLogxK

U2 - 10.2991/jnmp.2002.9.4.6

DO - 10.2991/jnmp.2002.9.4.6

M3 - Article

AN - SCOPUS:0036433671

VL - 9

SP - 455

EP - 463

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

SN - 1402-9251

IS - 4

ER -