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Volumn 53, Issue 4, 2001, Pages 715-755

Differential structure of orbit spaces

Author keywords

Accessible sets; Differential space; Poisson algebra; Proper action; Singular reduction; Symplectic manifolds

Indexed keywords


EID: 0035622635     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2001-029-1     Document Type: Article
Times cited : (36)

References (29)
  • 1
    • 0002881562 scopus 로고
    • A universal reduction procedure for Hamiltonian group actions
    • (ed. T. S. Ratiu), Birkhäuser, Boston
    • J. M. Arms, R. Cushman and M. J. Gotay, A universal reduction procedure for Hamiltonian group actions. In: The geometry of Hamiltonian systems (ed. T. S. Ratiu), Birkhäuser, Boston, 1991, 31-51.
    • (1991) The Geometry of Hamiltonian Systems , pp. 31-51
    • Arms, J.M.1    Cushman, R.2    Gotay, M.J.3
  • 2
    • 0000752863 scopus 로고
    • Symmetry and bifurcation of momentum mappings
    • J. Arms, J. E. Marsden and V. Moncrief, Symmetry and bifurcation of momentum mappings. Commun. Math. Phys. 78(1981), 455-478.
    • (1981) Commun. Math. Phys. , vol.78 , pp. 455-478
    • Arms, J.1    Marsden, J.E.2    Moncrief, V.3
  • 3
    • 0001541212 scopus 로고    scopus 로고
    • Proper group actions and symplectic stratified spaces
    • L. Bates and E. Lerman, Proper group actions and symplectic stratified spaces. Pacific J. Math. 191(1997), 201-229.
    • (1997) Pacific J. Math. , vol.191 , pp. 201-229
    • Bates, L.1    Lerman, E.2
  • 4
    • 0002023531 scopus 로고    scopus 로고
    • Lagrangian reduction, the Euler-Poincaré equations, and semidirect products
    • H. Cendra, D. D. Holm, J. E. Marsden and T. S. Ratiu, Lagrangian Reduction, the Euler-Poincaré Equations, and Semidirect Products. Trans. Amer. Math. Soc. 186(1998), 1-25.
    • (1998) Trans. Amer. Math. Soc. , vol.186 , pp. 1-25
    • Cendra, H.1    Holm, D.D.2    Marsden, J.E.3    Ratiu, T.S.4
  • 6
    • 0039789453 scopus 로고
    • On singular reduction of Hamiltonian systems
    • (ed. P. Donato), Birkhäuser, Boston
    • R. Cushman and R. Sjamaar, On singular reduction of Hamiltonian systems. In: Symplectic geometry and mathematical physics (ed. P. Donato), Birkhäuser, Boston, 1991, 114-128.
    • (1991) Symplectic Geometry and Mathematical Physics , pp. 114-128
    • Cushman, R.1    Sjamaar, R.2
  • 9
    • 0003358561 scopus 로고
    • Stratified Morse theory
    • Springer Verlag, New York
    • M. Goresky and R. MacPherson, Stratified Morse theory. Ergeb. der Math. 14, Springer Verlag, New York, 1988.
    • (1988) Ergeb. der Math. , vol.14
    • Goresky, M.1    MacPherson, R.2
  • 12
    • 0000757211 scopus 로고
    • Reduction of Poisson manifolds
    • J. E. Marsden and T. S. Ratiu, Reduction of Poisson manifolds. Lett. Math. Phys. 11(1986), 161-169.
    • (1986) Lett. Math. Phys. , vol.11 , pp. 161-169
    • Marsden, J.E.1    Ratiu, T.S.2
  • 13
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • J. E. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetry. Rep. Math. Phys. 5(1974), 121-130.
    • (1974) Rep. Math. Phys. , vol.5 , pp. 121-130
    • Marsden, J.E.1    Weinstein, A.2
  • 14
    • 0002681954 scopus 로고
    • Symmetries and integrals in mechanics
    • (ed. M. Piexoto), Academic Press, New York
    • K. Meyer, Symmetries and integrals in mechanics. In: Dynamical systems (ed. M. Piexoto), Academic Press, New York, 1973, 259-272.
    • (1973) Dynamical Systems , pp. 259-272
    • Meyer, K.1
  • 15
    • 0003626553 scopus 로고
    • Manifolds of differentiable mappings
    • Shiva Publishing, Nantwich
    • P. Michor, Manifolds of differentiable mappings. Shiva Mathematical Series 3, Shiva Publishing, Nantwich, 1980.
    • (1980) Shiva Mathematical Series , vol.3
    • Michor, P.1
  • 17
    • 0002083047 scopus 로고    scopus 로고
    • Singular reduction of Poisson manifolds
    • J.-P. Ortega and T. S. Ratiu, Singular reduction of Poisson manifolds. Lett. Math. Phys. 46(1998), 359-372.
    • (1998) Lett. Math. Phys. , vol.46 , pp. 359-372
    • Ortega, J.-P.1    Ratiu, T.S.2
  • 19
    • 0001441560 scopus 로고
    • On the existence of slices for actions of noncompact Lie groups
    • R. Palais, On the existence of slices for actions of noncompact Lie groups. Ann. of Math. 73(1961), 295-323.
    • (1961) Ann. of Math. , vol.73 , pp. 295-323
    • Palais, R.1
  • 20
    • 0039157452 scopus 로고
    • Unitary representations of solvable groups
    • L. Pukanski, Unitary representations of solvable groups. Ann. Sci. École Norm. Sup. 4(1971), 457-608.
    • (1971) Ann. Sci. École Norm. Sup. , vol.4 , pp. 457-608
    • Pukanski, L.1
  • 21
    • 0042805662 scopus 로고
    • Smooth functions invariant under the action of a compact Lie group
    • G. Schwarz, Smooth functions invariant under the action of a compact Lie group. Topology 14(1975), 63-68.
    • (1975) Topology , vol.14 , pp. 63-68
    • Schwarz, G.1
  • 22
    • 0040381637 scopus 로고
    • Abstract covariant derivative
    • R. Sikorski, Abstract covariant derivative. Colloq. Math. 18(1967), 151-172.
    • (1967) Colloq. Math. , vol.18 , pp. 151-172
    • Sikorski, R.1
  • 24
    • 85037288448 scopus 로고    scopus 로고
    • _, Wstȩp do geometrii różniczkowej. PWN, Warszawa, 1972. MR 57 7400.
    • MR , vol.57 , pp. 7400
  • 25
    • 0001229672 scopus 로고
    • Stratified symplectic spaces and reduction
    • R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction. Ann. of Math. 134(1991), 375-422.
    • (1991) Ann. of Math. , vol.134 , pp. 375-422
    • Sjamaar, R.1    Lerman, E.2
  • 26
    • 4243241350 scopus 로고
    • Yang-Mills and Dirac fields in a bag, constraints and reduction
    • J. Śniatycki, G. Schwarz and L. Bates, Yang-Mills and Dirac fields in a bag, constraints and reduction. Commun. Math. Phys. 168(1995), 441-453.
    • (1995) Commun. Math. Phys. , vol.168 , pp. 441-453
    • Śniatycki, J.1    Schwarz, G.2    Bates, L.3
  • 27
    • 84960607296 scopus 로고
    • Accessible sets, orbits and foliations with singularities
    • P. Stefan, Accessible sets, orbits and foliations with singularities. Proc. London Math. Soc. 29(1974), 699-713.
    • (1974) Proc. London Math. Soc. , vol.29 , pp. 699-713
    • Stefan, P.1
  • 28
    • 84968475624 scopus 로고
    • Orbits of families of vector fields and integrability of distributions
    • H. Sussmann, Orbits of families of vector fields and integrability of distributions. Trans. Amer. Math. Soc. 180(1973), 171-188.
    • (1973) Trans. Amer. Math. Soc. , vol.180 , pp. 171-188
    • Sussmann, H.1
  • 29
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined on closed sets
    • H. Whitney, Analytic extensions of differentiable functions defined on closed sets. Trans. Amer. Math. Soc. 36(1934), 63-89.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 63-89
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.