La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]

• 58-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 58-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 58-02 Research exposition (monographs, survey articles)
• 58-03 Historical (must also be assigned at least one classification number from Section 01)
• 58-04 Explicit machine computation and programs (not the theory of computation or programming)
• 58-06 Proceedings, conferences, collections, etc.
• 58-99 Global analysis, analysis on manifolds (not classified at a more specific level)
• 58Axx General theory of differentiable manifolds [See also 32Cxx]
• 58Bxx Infinite-dimensional manifolds
• 58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]
• 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]
  • 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
  • 58D07 Groups and semigroups of nonlinear operators [See also 17B65, 47H20]
  • 58D10 Spaces of imbeddings and immersions
  • 58D15 Manifolds of mappings [See also 46T10, 54C35]
  • 58D17 Manifolds of metrics (esp. Riemannian)
  • 58D19 Group actions and symmetry properties
  • 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]
  • 58D25 Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]
  • 58D27 Moduli problems for differential geometric structures
  • 58D29 Moduli problems for topological structures
  • 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
  • 58D99 None of the above, but in this section
• 58Exx Variational problems in infinite-dimensional spaces
• 58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
• 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]
• 58Kxx Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]
• 58Z05 Applications to physics

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