Differential geometrical relations for a class of formal series

Volume 40 / 1997

Alexandr Baranovitch Banach Center Publications 40 (1997), 279-287 DOI: 10.4064/-40-1-279-287


An extension of the category of local manifolds is considered. Instead of smooth mappings of neighbourhoods of linear spaces as morphisms we deal with formal operator power series (or formal maps). Analogues of the objects appearing on smooth manifolds and vector bundles (vector fields, sections of a bundle, exterior forms, the de Rham complex, connection, etc.) are considered in this way. All the examinations are carried out in algebraic language, for we do not care about the convergence of formal maps. It may be useful for the investigation of some nonlinear differential equations.


  • Alexandr Baranovitch

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