The Weil bundle TA Mn of an
n-dimensional smooth manifold Mn
determined by a local algebra A in the sense of A. Weil
carries a natural structure of an n-dimensional A-smooth
This allows ones to associate with TA Mn the series
Br(A)TA Mn , r=1,∞,
of A-smooth r-frame bundles.
As a set, Br(A)TA Mn consists
of r-jets of
A-smooth germs of diffeomorphisms (An,0)
We study the structure of A-smooth r-frame bundles.
In particular, we introduce the structure form of Br(A)TA Mn
and study its properties.
Next we consider some categories of m-parameter-dependent manifolds whose objects are trivial bundles Mn× Rm→ Rm, define (generalized) Weil bundles and higher order frame bundles of m-parameter-dependent manifolds and study the structure of these bundles. We also show that product preserving bundle functors on the introduced categories of m-parameter-dependent manifolds are equivalent to generalized Weil functors.
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