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Keywords:
generalized sections; Frölicher smoothness; connections
generalized sections; Frölicher smoothness; connections
Summary:
Smooth bundles, whose fibres are distribution spaces, are introduced according to the notion of smoothness due to Frölicher. Some fundamental notions of differential geometry, such as tangent and jet spaces, Frölicher-Nijenhuis bracket, connections and curvature, are suitably generalized. It is also shown that a classical connection on a finite-dimensional bundle naturally determines a connection on an associated distributional bundle.
References:
[Bo67] Boman J.: Differentiability of a function and of its composition with functions of one variable. Math. Scand. 20 (1967), 249–268. MR 0237728
[BLT75] Bogolubov N.N., Logunov A.A., Todorov I.T.: Introduction to Axiomatic Quantum Field Theory. Benjamin, Reading (1975). MR 0452277
[CK] Cabras A., Kolář I., - : Connections on some functional bundles. Czech. Math. J. 45, 120 (1995), 529–548. - On the iterated absolute differentiation on some functional bundles, Arch. Math. Brno 33 (1997), 23–35. - The universal connection of an arbitrary system, Ann. Mat. Pura e Appl. (IV) Vol. CLXXIV (1998), 1–11. MR 1464298 | Zbl 0851.58007
[Fr82] Frölicher A.: Smooth structures. LNM 962, Springer-Verlag 1982, 69–81. MR 0682945
[FK88] Frölicher A., Kriegl A.: Linear spaces and differentiation theory. John Wiley & Sons (1988). MR 0961256 | Zbl 0657.46034
[FN56] Frölicher A., Nijenhuis A.: Theory of vector valued differential forms, I. Indag. Math. 18 (1956), 338–359. MR 0082554
[JM] Jadczyk A., Modugno M., - : An outline of a new geometrical approach to Galilei general relativistic quantum mechanics. in Proc. XXI Int. Conf. on Differential Geometric Methods in Theoretical Physics, Tianjin 5-9 June 1992, ed. Yang, C.N. et al., pp 543–556, World Scientific, Singapore, 1992. - A scheme for Galilei general relativistic quantum mechanics, in General Relativity and Gravitational Physics, M. Cerdonio, R. D’Auria, M. Francaviglia, G. Magnano eds., World Scientific, Singapore (1994), 319–337. MR 1349843
[KM97] Kriegl A., Michor P.: The convenient setting of global analysis. American Mathematical Society 1997. MR 1471480 | Zbl 0889.58001
[KMS93] Kolář I., Michor P., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag 1993. MR 1202431
[MK98] Modugno M., Kolář I.: The Frölicher-Nijenhuis bracket on some functional spaces. Ann. Pol. Math. LXVIII.2 (1998), 97–106. MR 1610540 | Zbl 0982.53024
[MM84] Mangiarotti L., Modugno M.: Graded Lie algebras and connections on fibred spaces. J. Math. Pures Appl. 83 (1984), 111–120. MR 0776913
[Sc66] Schwartz L.: Théorie des distributions. Hermann, Paris 1966. MR 0209834 | Zbl 0149.09501
[Sl86] Slovák J.: Smooth structures on fibre jet spaces. Czech. Math. J. 36, 111 (1986), 358–375. MR 0847766
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