Topology of quantizable dynamical systems and the algebra of observables

Hurt, Norman E.

Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 16 (1972) no. 3, pp. 203-217.

[1] J.F. Adams, On the nonexistence of elements of Hopf invariant one (Ann. of Math., vol. 72, 1960. p. 20-104). | MR | Zbl

[2] J. Adem, Relations on iterated reduced powers (Proc. Nat. Acad. Sci. U. S. A., vol. 39, 1953, p. 636-638). | MR | Zbl

[3] A.C. Allamigeon, Propriétés globales des espaces de Riemann harmoniques (Ann. Inst. Fourier, t. 15, 1965, p. 91-132). | Numdam | MR | Zbl

[4] R.L. Bishop and S.I. Goldberg, Rigidity of positively curved Kähler manifolds (Proc. Nat. Acad. Sci. U. S. A., vol. 54, 1965, p. 1037-1041); On the second cohomology group of a Kähler manifold of positive sectional curvature (Proc. Amer. Math. Soc., vol. 16, 1965, p. 119-122). | MR | Zbl

[5] D.E. Blair and S.I. Goldberg, Topology of almost contact manifolds (J. Diff. Geom., vol. 1, 1967, p. 347-354). | MR | Zbl

[6] D. Bohm, B.J. Hiley and A.E.G. Stuart, Inter. J. Theor. Phys., 3, 1970, p. 171; B.J. Hiley and A.E.G. Stuart, Phase Space, Fibre bundles and current algebras (Inter. J. Theor. Phys., vol. 4, 1971, p. 247-265). | MR

[7] W.M. Boothby and H.C. Wang, On contact manifolds (Ann. of Math., vol. 68, 1968, p. 721-734). | MR | Zbl

[8] R. Bott, On manifolds all of whose geodesics are closed (Ann. of Math., 60, 1954, p. 375-382). | MR | Zbl

[9] W. Browder, Surgery and the theory of differentiable transformation groups (Proceedings of the Conference on Transformation groups) (Springer-Verlag, 1968), p. 1-46. | MR | Zbl

[10] E. Cartan, Sur les variétés à connexion projective (Bull. Soc. math. Fr., t. 52, 1924, p. 205-241). | JFM | Numdam | MR

[11] P. Dazord, Variétés finslériennes à géodésiques fermées (C. R. Acad. Sc., Paris, t. 266, série A, p. 348-350; Propriétés globales des géodésiques des espaces Finsler (Thesis, 1969). | MR | Zbl

[12] J. Eells and N. Kuiper, Manifolds which are like projective planes (Public. Math. I. H. E. S., vol. 14, 1962, p. 5-46). | Numdam | MR | Zbl

[13] A. Gleason, Spaces with a compact Lie group of transformations (Proc. Amer. Math. Soc., vol. 1, 1950, p. 35-43). | MR | Zbl

[14] S.I. Goldberg, Rigidity of positively curved contact manifolds (J. London Math. Soc., vol. 42, 1967, p. 257-263). | MR | Zbl

[15] S.I. Goldberg, On the topology of compact contact manifolds (Tohoku Math. J., vol. 20, 1968, p. 106-110). | MR | Zbl

[16] R.C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables (Prentice-Hall, Englewood Cliffs, 1965). | MR | Zbl

[17] M. Harada, On the curvature of Sasakian manifolds (Bull. Yamagata Univ., vol. 7, 1969, p. 97-106). | MR

[18] M. Harada, On the minimal diameter of Sasakian manifolds (Ibid., vol. 7, No. 3, 1970, p. 191-203). | MR

[19] W.C. Hsiang, A note on free differentiable actions of S1 and S3 on homotopy spheres (Ann. of Math., vol. 83, 1966, p. 266-272). | MR | Zbl

[20] W.C. Hsiang and W.Y. Hsiang, Some free differentiable actions on 11-spheres (Quart. J. Math., vol. 15, 1964, p. 371-374). | MR | Zbl

[21] S.T. Hu, Homotopy Theory (Academic Press, New York, 1959). | MR | Zbl

[22] N.E. Hurt, Remarks on Canonical Quantization (Il Nuovo Cimento, vol. 55 A, 1968, p. 534-542). | Zbl

[23] N.E. Hurt, Remarks on Morse Theory in Canonical Quantization (J. Math. Phys., vol. 11, 1970, p. 539-551). | MR

[24] N.E. Hurt, Examples in Quantizable Dynamical Systems, II (Lettere al Nuovo Cimento, vol. 3, 1970, p. 137-138).

[25] N.E. Hurt, Differential Geometry of Canonical Quantization (Ann. Inst. H. Poincaré, vol. XIV, No.2, 1971, p. 153-170). | Numdam | MR | Zbl

26] N.E. Hurt, A classification theory of quantizable dynamical systems (Report on Math. Phys., vol. 2, 1971, p. 211-220). | MR | Zbl

[27] M. Kervaire, A manifold which does not admit any differentiable structure (Comm. Math. Helv., vol. 34, 1960, p. 257-270). | MR | Zbl

[28] M. Kervaire and J.W. Milnor, Groups of Homotopy Spheres, I (Ann. of Math., vol. 77, 1963), p. 504-537). | MR | Zbl

[29] W. Klingenberg, Manifolds with restricted conjugate locus (Ann. of Math., vol. 78, 1963, p. 527-547). | MR | Zbl

[30] K. Kodaira, On Kähler varieties of restricted type (Ann. of Math., vol., 60, 1954, p. 28-48). | MR | Zbl

[31] R. Lee, Nonexistence of Free differentiable actions of S1 and Z2 on Homotopy spheres, [9], p. 208-209. | MR | Zbl

[32] G. Mackey, Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963). | Zbl

[33] J. Milnor, On manifolds homeomorphic to the 7-sphere (Ann. of Math., vol. 64, 1956, p. 399-405). | MR | Zbl

[34] J. Milnor, On the existence of a connection with curvature zero (Comm. Math. Helv., vol. 32, 1957, p. 215-223). | MR | Zbl

[35] C.W. Misner and J.A. Wheeler, Gravitation, Electromagnetism Unquantized Charge, and Mass as properties of curved empty space (Ann. of Phys., vol. 2, 1957, p. 525-660). | MR | Zbl

[36] D. Montgomery and C.T. Yang, Differentiable Actions on homotopy seven sphere, I (Trans Amer. Math. Soc., vol. 122, 1966, p. 480-498). | MR | Zbl

[37] D. Montgomery and C.T. Yang, Differentiable Actions on homotopy seven sphere, II, [9], p. 125-133. | MR | Zbl

[38] J.R. Munkres, Obstructions to smoothing a piecewise differentiable homeomorphism (Ann. of Math., vol. 72, 1960, p. 521-554). | MR | Zbl

[39] J.R. Munkres, Elementary Differential Topology (Princeton University Press, 1966). | MR | Zbl

[40] H. Nakagawa, A note on theorems of Bott and Samelson (J. Math. of Kyoto Univ., vol., 7, 1967, p. 205-220); Riemannian manifolds with many geodesic loops (J. Math. Soc. Japan, vol. 20, 1968, p. 648-654). | MR | Zbl

[41] G. Reeb, Sur certaines propriétés topologiques des trajectoires des systèmes dynamiques (Mém. Acad. roy. Belgique, Cl. Sc., vol. 27, n° 9, 1952, p. 1-64). | MR | Zbl

[42] G. Reeb, Trois problèmes de la théory des systèmes dynamique, (Colloq. Géom. Diff. Global) (C. B. R. M., 1958), p. 89-94. | MR | Zbl

[43] H. Samelson, On manifolds with many closed geodesics (Portugaliae Math., vol. 22, 1963, p. 193-196). | MR | Zbl

[44] S. Smale, Generalized Poincaré conjecture in dimensions greater than four (Ann. of Math., vol. 74, 1961, p. 391-406). | MR | Zbl

[45] S. Smale, Stable manifolds for differential equations and diffeomorphisms (Ann. Scola Normu. Sup. Pisa, vol. 17, 1963, p. 97-116). | Numdam | MR | Zbl

[46] J.M. Souriau, Structure des systèmes dynamiques (Dunod, Paris, 1970). | MR | Zbl

[47] E. Spainier, Algebraic Topology (Mc Craw-Hill, New York, 1966). | Zbl

[48] J. Stallings, The piecewise-linear structure of euclidean space (Proc. Cambridge Phil. Soc., vol. 58, 1962, p. 481-488). | MR | Zbl

[49] N. Steenrod, The Topology of Fiber Bundles (Princeton University Press, Princeton, 1951). | Zbl

[50] S. Tanno, The topology of contact Riemannian manifolds (Ill. J. Math., vol. 12, 1968, p. 700-717). | MR | Zbl

[51] H.O. Singh Varma, Homogeneous manifolds all of whose geodesics are closed (Indag. Math., vol. 48, 1965, p. 813-819). | MR | Zbl