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On the torsion of linear higher order connections

Ivan Kolář — 2003

Open Mathematics

For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.

Functorial prolongations of Lie groupoids

Ivan Kolář — 2007

Banach Center Publications

For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.

Natural maps depending on reductions of frame bundles

Ivan Kolář — 2011

Annales Polonici Mathematici

We clarify how the natural transformations of fiber product preserving bundle functors on m can be constructed by using reductions of the rth order frame bundle of the base, m being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.

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