| 58-XX | | Prev: 57 | Up: Top | Next: 60 | |
| Global analysis, analysis on manifolds [xref: 53Cxx, 57R57] | |
| {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.
| |
58Axx
| General theory of differentiable manifolds [See also 32Cxx]
[xref: 70G45]
| 58A03 |
Topos-theoretic approach to differentiable manifolds
| 58A05 |
Differentiable manifolds, foundations
| 58A07 |
Real-analytic and Nash manifolds [See also 14P20, 32C07]
[xref: 14P20, 32C05]
| 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)
[xref: 35B60]
| 58A17 |
Pfaffian systems
[xref: 35B60]
| 58A20 |
Jets
| 58A25 |
Currents [See also 32C30, 53C65]
[xref: 49Q15]
| 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]
[xref: 14M30, 32C11, 46S60]
| 58A99 |
None of the above, but in this section
| |
58Bxx
| Infinite-dimensional manifolds
[xref: 32K05, 46T05, 57N20]
| 58B05 |
Homotopy and topological questions
| 58B10 |
Differentiability questions
| 58B12 |
Questions of holomorphy [See also 32-XX, 46G20]
[xref: 46G20]
| 58B15 |
Fredholm structures [See also 47A53]
[xref: 47A53]
| 58B20 |
Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]
[xref: 53C20, 53C60]
| 58B25 |
Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]
[xref: 22E65]
| 58B32 |
Geometry of quantum groups
[xref: 46L85, 46L87, 46L89]
| 58B34 |
Noncommutative geometry (à la Connes)
[xref: 46L85, 46L87, 46L89, 81T75, 83C65]
| 58B99 |
None of the above, but in this section
| |
58Cxx
| Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]
[xref: 26E15, 26E20, 46Txx]
| 58C05 |
Real-valued functions
| 58C06 |
Set valued and function-space valued mappings [See also 47H04, 54C60]
[xref: 47H04, 49J53, 54C60]
| 58C07 |
Continuity properties of mappings
| 58C10 |
Holomorphic maps [See also 32-XX]
[xref: 46G20]
| 58C15 |
Implicit function theorems; global Newton methods
[xref: 47J07]
| 58C20 |
Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]
[xref: 46G05, 49J50]
| 58C25 |
Differentiable maps
[xref: 26E10, 32K15, 46G05]
| 58C30 |
Fixed point theorems on manifolds [See also 47H10]
[xref: 47H10, 47H11, 65H20]
| 58C35 |
Integration on manifolds; measures on manifolds [See also 28Cxx]
[xref: 28C20, 28Cxx, 46F25, 49Q15]
| 58C40 |
Spectral theory; eigenvalue problems [See also 47J10, 58E07]
[xref: 65H17]
| 58C50 |
Analysis on supermanifolds or graded manifolds
[xref: 32K07, 46S60, 49J52]
| 58C99 |
None of the above, but in this section
| |
58Dxx
| Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]
[xref: 46T05, 46Txx, 81T45]
| 58D05 |
Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
[xref: 22E67, 57Sxx, 58B25]
| 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]
[xref: 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]
[xref: 28C20, 28Cxx]
| 58D25 |
Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]
[xref: 34Gxx, 35R15, 47J35]
| 58D27 |
Moduli problems for differential geometric structures
| 58D29 |
Moduli problems for topological structures
[xref: 81T70]
| 58D30 |
Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
[xref: 81S40]
| 58D99 |
None of the above, but in this section
| |
58Exx
| Variational problems in infinite-dimensional spaces
[xref: 47J30, 49Qxx]
| 58E05 |
Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
| 58E07 |
Abstract bifurcation theory
[xref: 47J15, 58C40, 65H17]
| 58E09 |
Group-invariant bifurcation theory
[xref: 47J15]
| 58E10 |
Applications to the theory of geodesics (problems in one independent variable)
[xref: 53C22]
| 58E11 |
Critical metrics
| 58E12 |
Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
[xref: 49Q05]
| 58E15 |
Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
[xref: 81T13]
| 58E17 |
Pareto optimality, etc., applications to economics [See also 90C29]
| 58E20 |
Harmonic maps [See also 53C43], etc.
[xref: 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
| |
| 1991 | 58F08| now 37B15, 37C99, 37E99
Point-mapping properties, iterations, completeness; dynamics of cellular automata
| 58Hxx
| Pseudogroups, differentiable groupoids and general structures on manifolds
[xref: 35B60, 35Nxx]
| 58H05 |
Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
[xref: 22A22, 22E05, 22E65]
| 58H10 |
Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
[xref: 22E41, 32G05, 57R32]
| 58H15 |
Deformations of structures [See also 32Gxx, 58J10]
[xref: 32G05]
| 58H99 |
None of the above, but in this section
| |
58Jxx
| Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]
[xref: 35Jxx, 35Nxx, 47F05, 47G30, 47Gxx]
| 58J05 |
Elliptic equations on manifolds, general theory [See also 35-XX]
| 58J10 |
Differential complexes [See also 35Nxx]; elliptic complexes
[xref: 35Jxx, 35N15, 35Nxx, 58H15]
| 58J15 |
Relations with hyperfunctions
[xref: 32C38, 35A27, 35Nxx, 35S35, 46F15]
| 58J20 |
Index theory and related fixed point theorems [See also 19K56, 46L80]
[xref: 18G60, 19K56, 35Jxx, 47A53]
| 58J22 |
Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
[xref: 18G60, 19K35, 19K56, 46L80, 46L85, 46L87, 46L89]
| 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
[xref: 35Kxx]
| 58J37 |
Perturbations; asymptotics
| 58J40 |
Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]
[xref: 35Sxx]
| 58J42 |
Noncommutative global analysis, noncommutative residues
| 58J45 |
Hyperbolic equations [See also 35Lxx]
[xref: 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.)
[xref: 53C21]
| 58J65 |
Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
[xref: 60Hxx, 60J60, 60J65]
| 58J70 |
Invariance and symmetry properties [See also 35A30]
[xref: 35A30]
| 58J72 |
Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]
[xref: 35A30]
| 58J90 |
Applications
| 58J99 |
None of the above, but in this section
| |
58Kxx
| Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]
[xref: 14B05, 32S60, 32Sxx, 35L67]
| 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
| |