XXXII Workshop on Geometric Methods in Physics | 30.06-6.07.2013 |

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## Hovhannes Khudaverdian## Operator pencils, densities and equivariant geometryWe consider pencil lifting maps from operators on densities of given weight to operator pencils defined on densities of all weights. In general, such a map can be defined and it can be defined uniquely, only on operators of order \leq 2, if we impose a natural condition that the lifting is equivariant with respect to the group of all diffeomorphisms of the base manifold. We explain the geometrical meaning of such a map. Then we analyze the existence and uniqueness of lifting maps defined on operators of all orders in the case if lifting map is equivariant with respect to a smaller group, such as the group of diffeomorphisms preserving volume form, or the group of diffeomorphisms preserving a projective structure. |

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University of Bialystok |

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