Previous |  Up |  Next

Article

Title: Product preserving functors of infinite-dimensional manifolds (English)
Author: Kriegl, Andreas
Author: Michor, Peter W.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 32
Issue: 4
Year: 1996
Pages: 289-306
Summary lang: English
.
Category: math
.
Summary: The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of $C^\infty $-algebras. (English)
Keyword: product preserving functors
Keyword: convenient vector spaces
Keyword: $C^\infty$-algebras
MSC: 58B99
idZBL: Zbl 0881.58010
idMR: MR1441400
.
Date available: 2008-06-06T21:31:34Z
Last updated: 2012-05-10
Stable URL: http://hdl.handle.net/10338.dmlcz/107582
.
Reference: [1] Eck, D. J.: Product preserving functors on smooth manifolds.J. Pure and Applied Algebra 42 (1986), 133–140. Zbl 0615.57019, MR 0857563
Reference: [2] Frölicher, A., Kriegl, A.: Linear spaces and differentiation theory.Pure and Applied Mathematics, J. Wiley, Chichester, 1988. MR 0961256
Reference: [3] Kainz, G., Kriegl, A., Michor, P. W.: $C^\infty $-algebras from the functional analytic viewpoint.J. pure appl. Algebra 46 (1987), 89-107. MR 0894394
Reference: [4] Kainz, G., Michor, P. W.: Natural transformations in differential geometry.Czechoslovak Math. J. 37 (1987), 584-607. MR 0913992
Reference: [5] Kolář, I.: Covariant approach to natural transformations of Weil functors.Comment. Math. Univ. Carolin. 27 (1986), 723–729. MR 0874666
Reference: [6] Kolář, I.,; Michor, P. W., Slovák, J.: Natural operations in differential geometry.Springer-Verlag, Berlin, Heidelberg, New York, 1993, pp. vi+434. MR 1202431
Reference: [7] Kriegl, A., Michor, P. W.: A convenient setting for real analytic mappings.Acta Mathematica 165 (1990), 105–159. MR 1064579
Reference: [8] Kriegl, A., Michor, P. W.: Aspects of the theory of infinite dimensional manifolds.Differential Geometry and Applications 1 (1991), 159–176. MR 1244442
Reference: [9] Kriegl, A., Michor, P. W.: Regular infinite dimensional Lie groups.to appear, J. Lie Theory (1997). MR 1450745
Reference: [10] Kriegl, A., Michor, P. W.: The Convenient Setting for Global Analysis.to appear, Surveys and Monographs, AMS, Providence, 1997. MR 1471480
Reference: [11] Kriegl, A., Nel, L. D.: A convenient setting for holomorphy.Cahiers Top. Géo. Diff. 26 (1985), 273–309. MR 0796352
Reference: [12] Lawvere, F. W.: Categorical dynamics.Lectures given 1967 at the University of Chicago, reprinted in, Topos Theoretical Methods in Geometry, A. Kock (ed.), Aarhus Math. Inst. Var. Publ. Series 30, Aarhus Universitet, 1979. Zbl 0403.18005, MR 0552656
Reference: [13] Luciano, O. O.: Categories of multiplicative functors and Weil’s infinitely near points.Nagoya Math. J. 109 (1988), 69–89. Zbl 0661.58007, MR 0931952
Reference: [14] Michor, P. W., Vanžura, J.: Characterizing algebras of smooth functions on manifolds.to appear, Comm. Math. Univ. Carolinae (Prague).
Reference: [15] Milnor, J.: Remarks on infinite dimensional Lie groups.Relativity, Groups, and Topology II, Les Houches, 1983, B.S. DeWitt, R. Stora, Eds., Elsevier, Amsterdam, 1984. Zbl 0594.22009, MR 0830252
Reference: [16] Moerdijk, I., Reyes G. E.: Models for smooth infinitesimal analysis.Springer-Verlag, Heidelberg Berlin, 1991. MR 1083355
Reference: [17] Moerdijk, I., Reyes G. E.: Rings of smooth funcions and their localizations, I.J. Algebra 99 (1986), 324–336. MR 0837547
Reference: [18] Morimoto, A.: Prolongations of connections to bundles of infinitely near points.J. Diff. Geom. 11 (1976), 479–498. MR 0445422
Reference: [19] Moerdijk, I., Ngo Van Que, Reyes G. E.: Rings of smooth funcions and their localizations, II.Mathematical logic and theoretical computer science, D.W. Kueker, E.G.K. Lopez-Escobar, C.H. Smith (eds.), Marcel Dekker, New York, Basel, 1987. MR 0930685
Reference: [20] Omori, H., Maeda, Y., Yoshioka, A.: On regular Fréchet Lie groups IV. Definitions and fundamental theorems.Tokyo J. Math. 5 (1982), 365–398. MR 0688131
Reference: [21] Weil, A.: Théorie des points proches sur les variétés differentielles.Colloque de topologie et géométrie différentielle, Strasbourg, 1953, pp. 111–117. MR 0061455
.

Files

Files Size Format View
ArchMathRetro_032-1996-4_5.pdf 353.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo