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A remark on the topology of higher order frames. (English) Zbl 1061.53017
Slovák, Jan (ed.) et al., The proceedings of the 23th winter school “Geometry and physics”, Srní, Czech Republic, January 18–25, 2003. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 72, 171-176 (2004).
A \(k\)th-order \(G\)-structure on a differentiable manifold \(M\) may be considered as a subbundle of the \(k\)th-order frame bundle \(F^k(M, GL_k)\) of \(M\). The author studies the bundle projection \(P^2\to P^1\) and the homomorphism projection \(G^2\to G^1\) of a second- and first-order \(G\)-structure on \(M\), \(P^2(M, G^2)\) and \(P^1(M, G^1)\), respectively. The existence of the second-order flat lifts is proved and certain characteristic classes are defined in terms of a gauge sequence worked out by the author in [Proc. (Conf. of DGA Brno, 1998), 273–283, Masaryk Univ., Brno, 1999] or [Second- order connections via gauge sequence, preprint; per bibs.].
For the entire collection see [Zbl 1034.53002].
53C10 \(G\)-structures
57R20 Characteristic classes and numbers in differential topology