55-XX | Prev: 54 | Up: Top | Next: 57 |
Algebraic topology
55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
55-01 Instructional exposition (textbooks, tutorial papers, etc.)
55-02 Research exposition (monographs, survey articles)
55-03 Historical (must also be assigned at least one classification number from Section 01)
55-04 Explicit machine computation and programs (not the theory of computation or programming)
55-06 Proceedings, conferences, collections, etc.
55Mxx Classical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx}   [xref: 54F35]
55M05 Duality
55M10 Dimension theory [See also 54F45]   [xref: 54F45]
55M15 Absolute neighborhood retracts [See also 54C55]   [xref: 54C55]
55M20 Fixed points and coincidences [See also 54H25]   [xref: 47H10, 54H25]
55M25 Degree, winding number   [xref: 47H11]
55M30 Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
55M35 Finite groups of transformations (including Smith theory) [See also 57S17]
55M99 None of the above, but in this section
55Nxx Homology and cohomology theories [See also 57Txx]   [xref: 18Gxx, 54F35]
55N05 Cech types   [xref: 55Q70]
55N07 Steenrod-Sitnikov homologies   [xref: 55Q70]
55N10 Singular theory
55N15 $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
55N20 Generalized (extraordinary) homology and cohomology theories
55N22 Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]   [xref: 14L05, 19K33, 19L41, 57R77, 57R90]
55N25 Homology with local coefficients, equivariant cohomology
55N30 Sheaf cohomology [See also 18F20, 32C35, 32L10]   [xref: 18F20, 32C35, 32L10]
55N33 Intersection homology and cohomology
55N34 Elliptic cohomology
55N35 Other homology theories
55N40 Axioms for homology theory and uniqueness theorems
55N45 Products and intersections
55N91 Equivariant homology and cohomology [See also 19L47]   [xref: 19L47]
55N99 None of the above, but in this section
55Pxx Homotopy theory {For simple homotopy type, see 57Q10}
55P05 Homotopy extension properties, cofibrations
55P10 Homotopy equivalences
55P15 Classification of homotopy type
55P20 Eilenberg-Mac Lane spaces
55P25 Spanier-Whitehead duality
55P30 Eckmann-Hilton duality
55P35 Loop spaces
55P40 Suspensions
55P42 Stable homotopy theory, spectra
55P43 Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
55P45 ${H}$-spaces and duals
55P47 Infinite loop spaces
55P48 Loop space machines, operads [See also 18D50]   [xref: 18D50]
55P55 Shape theory [See also 54C56, 55Q07]   [xref: 54C56, 57N25]
55P57 Proper homotopy theory
55P60 Localization and completion
55P62 Rational homotopy theory
55P65 Homotopy functors
55P91 Equivariant homotopy theory [See also 19L47]   [xref: 19L47]
55P92 Relations between equivariant and nonequivariant homotopy theory
55P99 None of the above, but in this section
55Qxx Homotopy groups
55Q05 Homotopy groups, general; sets of homotopy classes
55Q07 Shape groups   [xref: 55P55, 57N25]
55Q10 Stable homotopy groups
55Q15 Whitehead products and generalizations
55Q20 Homotopy groups of wedges, joins, and simple spaces
55Q25 Hopf invariants
55Q35 Operations in homotopy groups
55Q40 Homotopy groups of spheres
55Q45 Stable homotopy of spheres
55Q50 $J$-morphism [See also 19L20]   [xref: 19L20]
55Q51 $v_n$-periodicity
55Q52 Homotopy groups of special spaces
55Q55 Cohomotopy groups
55Q70 Homotopy groups of special types [See also 55N05, 55N07]
55Q91 Equivariant homotopy groups [See also 19L47]   [xref: 19L47]
55Q99 None of the above, but in this section
55Rxx Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]   [xref: 18F15, 32Lxx, 46L80, 46M20, 57R22]
55R05 Fiber spaces
55R10 Fiber bundles
55R12 Transfer
55R15 Classification
55R20 Spectral sequences and homology of fiber spaces [See also 55Txx]   [xref: 55Txx, 57T35]
55R25 Sphere bundles and vector bundles
55R35 Classifying spaces of groups and ${H}$-spaces
55R37 Maps between classifying spaces
55R40 Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
55R45 Homology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity
55R50 Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
55R55 Fiberings with singularities
55R60 Microbundles and block bundles [See also 57N55, 57Q50]   [xref: 57N55, 57Q50]
55R65 Generalizations of fiber spaces and bundles
55R70 Fibrewise topology
55R80 Discriminantal varieties, configuration spaces
55R91 Equivariant fiber spaces and bundles [See also 19L47]   [xref: 19L47]
55R99 None of the above, but in this section
55Sxx Operations and obstructions
55S05 Primary cohomology operations
55S10 Steenrod algebra
55S12 Dyer-Lashof operations
55S15 Symmetric products, cyclic products
55S20 Secondary and higher cohomology operations
55S25 $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
55S30 Massey products
55S35 Obstruction theory
55S36 Extension and compression of mappings
55S37 Classification of mappings
55S40 Sectioning fiber spaces and bundles
55S45 Postnikov systems, $k$-invariants
55S91 Equivariant operations and obstructions [See also 19L47]   [xref: 19L47]
55S99 None of the above, but in this section
55Txx Spectral sequences [See also 18G40, 55R20]   [xref: 18G40, 55R20]
55T05 General
55T10 Serre spectral sequences
55T15 Adams spectral sequences
55T20 Eilenberg-Moore spectral sequences [See also 57T35]   [xref: 57T35]
55T25 Generalized cohomology
55T99 None of the above, but in this section
55Uxx Applied homological algebra and category theory [See also 18Gxx]   [xref: 18Gxx, 57T30]
55U05 Abstract complexes
55U10 Simplicial sets and complexes   [xref: 13F55, 18G30]
55U15 Chain complexes
55U20 Universal coefficient theorems, Bockstein operator
55U25 Homology of a product, Künneth formula   [xref: 18G15]
55U30 Duality
55U35 Abstract and axiomatic homotopy theory
55U40 Topological categories, foundations of homotopy theory
55U99 None of the above, but in this section

Version 2000