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Navegando por la clasificación temática MSC 2000: 58 · Global analysis, analysis on manifolds
58 Global analysis, analysis on manifolds
  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
  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)
  58A General theory of differentiable manifolds [See also 32Cxx]
    58A03 Topos-theoretic approach to differentiable manifolds
    58A05 Differentiable manifolds, foundations
    58A07 Real-analytic and Nash manifolds [See also 14P20, 32C07]
    58A10 Differential forms
    58A12 de Rham theory [See also 14Fxx]
    58A14 Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]
    58A15 Exterior differential systems (Cartan theory)
    58A17 Pfaffian systems
    58A20 Jets
    58A25 Currents [See also 32C30, 53C65]
    58A30 Vector distributions (subbundles of the tangent bundles)
    58A32 Natural bundles
    58A35 Stratified sets [See also 32S60]
    58A40 Differential spaces
    58A50 Supermanifolds and graded manifolds [See also 14A22, 32C11]
    58A99 None of the above, but in this section
  58B Infinite-dimensional manifolds
    58B05 Homotopy and topological questions
    58B10 Differentiability questions
    58B12 Questions of holomorphy [See also 32-XX, 46G20]
    58B15 Fredholm structures [See also 47A53]
    58B20 Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]
    58B25 Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]
    58B32 Geometry of quantum groups
    58B34 Noncommutative geometry (à la Connes)
    58B99 None of the above, but in this section
  58C Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]
    58C05 Real-valued functions
    58C06 Set valued and function-space valued mappings [See also 47H04, 54C60]
    58C07 Continuity properties of mappings
    58C10 Holomorphic maps [See also 32-XX]
    58C15 Implicit function theorems; global Newton methods
    58C20 Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]
    58C25 Differentiable maps
    58C30 Fixed point theorems on manifolds [See also 47H10]
    58C35 Integration on manifolds; measures on manifolds [See also 28Cxx]
    58C40 Spectral theory; eigenvalue problems [See also 47J10, 58E07]
    58C50 Analysis on supermanifolds or graded manifolds
    58C99 None of the above, but in this section
  58D 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
  58E Variational problems in infinite-dimensional spaces
    58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
    58E07 Abstract bifurcation theory
    58E09 Group-invariant bifurcation theory
    58E10 Applications to the theory of geodesics (problems in one independent variable)
    58E11 Critical metrics
    58E12 Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
    58E15 Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13]
    58E17 Pareto optimality, etc., applications to economics [See also 90C29]
    58E20 Harmonic maps [See also 53C43]
    58E25 Applications to control theory [See also 49-XX, 93-XX]
    58E30 Variational principles
    58E35 Variational inequalities (global problems)
    58E40 Group actions
    58E50 Applications
    58E99 None of the above, but in this section
  58H Pseudogroups, differentiable groupoids and general structures on manifolds
    58H05 Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
    58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
    58H15 Deformations of structures [See also 32Gxx, 58J10]
    58H99 None of the above, but in this section
  58J Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]
    58J05 Elliptic equations on manifolds, general theory [See also 35-XX]
    58J10 Differential complexes [See also 35Nxx]
    58J15 Relations with hyperfunctions
    58J20 Index theory and related fixed point theorems [See also 19K56, 46L80]
    58J22 Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
    58J26 Elliptic genera
    58J28 Eta-invariants, Chern-Simons invariants
    58J30 Spectral flows
    58J32 Boundary value problems on manifolds
    58J35 Heat and other parabolic equation methods
    58J37 Perturbations; asymptotics
    58J40 Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]
    58J42 Noncommutative global analysis, noncommutative residues
    58J45 Hyperbolic equations [See also 35Lxx]
    58J47 Propagation of singularities; initial value problems
    58J50 Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
    58J52 Determinants and determinant bundles, analytic torsion
    58J53 Isospectrality
    58J55 Bifurcation [See also 35B32]
    58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)
    58J65 Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
    58J70 Invariance and symmetry properties [See also 35A30]
    58J72 Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]
    58J90 Applications
    58J99 None of the above, but in this section
  58K Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]
    58K05 Critical points of functions and mappings
    58K10 Monodromy
    58K15 Topological properties of mappings
    58K20 Algebraic and analytic properties of mappings
    58K25 Stability
    58K30 Global theory
    58K35 Catastrophe theory
    58K40 Classification; finite determinacy of map germs
    58K45 Singularities of vector fields, topological aspects
    58K50 Normal forms
    58K55 Asymptotic behavior
    58K60 Deformation of singularities
    58K65 Topological invariants
    58K70 Symmetries, equivariance
    58K99 None of the above, but in this section
  58Z05 Applications to physics

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