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1992 | 57 | 2 | 105-120
Tytuł artykułu

Continuity of projections of natural bundles

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Języki publikacji
EN
Abstrakty
EN
This paper is a contribution to the axiomatic approach to geometric objects. A collection of a manifold M, a topological space N, a group homomorphism E: Diff(M) → Homeo(N) and a function π: N → M is called a quasi-natural bundle if (1) π ∘ E(f) = f ∘ π for every f ∈ Diff(M) and (2) if f,g ∈ Diff(M) are two diffeomorphisms such that f|U = g|U for some open subset U of M, then E(f)|π^{-1}(U) = E(g)|π^{-1}(U). We give conditions which ensure that π: N → M is continuous. In particular, if (M,N,E,π) is a quasi-natural bundle with N Hausdorff, then π is continuous. Using this result, we classify (quasi) prolongation functors with compact fibres.
Rocznik
Tom
57
Numer
2
Strony
105-120
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-06-15
poprawiono
1991-05-10
Twórcy
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
  • [1] J. Aczél und S. Gołąb, Funktionalgleichungen der Theorie der geometrischen Objekte, PWN, Warszawa 1960.
  • [2] D. B. A. Epstein and W. P. Thurston, Transformation groups and natural bundles, Proc. London Math. Soc. (3) 38 (1979), 219-236.
  • [3] J. Gancarzewicz, Differential Geometry, Bibl. Mat. 64, Warszawa 1987 (in Polish).
  • [4] J. Gancarzewicz, Liftings of functions and vector fields to natural bundles, Dissertationes Math. 212 (1983).
  • [5] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, Springer, New York 1973.
  • [6] I. Kolář, Functorial prolongations of Lie groups and their actions, Časopis Pěst. Mat. 108 (1983), 289-293.
  • [7] K. Masuda, Homomorphism of the Lie algebras of vector fields, J. Math. Soc. Japan 28 (1976), 506-528.
  • [8] W. M. Mikulski, Locally determined associated spaces, J. London Math. Soc. (2) 32 (1985), 357-364.
  • [9] D. Montgomery and L. Zippin, Transformation Groups, Interscience, New York 1955.
  • [10] A. Nijenhuis, Natural bundles and their general properties, in: Diff. Geom. in honor of K. Yano, Kinokuniya, Tokyo 1972, 317-334.
  • [11] R. S. Palais and C. L. Terng, Natural bundles have finite order, Topology 16 (1978), 271-277.
  • [12] S. E. Salvioli, On the theory of geometric objects, J. Differential Geom. 7(1972), 257-278.
  • [13] J. Slovák, Smooth structures on fibre jet spaces, Czechoslovak Math. J. 36 (111) (1986), 358-375.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv57z2p105bwm
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