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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.
1970 55Axx now .....   Low-dimensional topology
1970 55A05 now .....   Fundamental group, presentation, free differential calculus
1970 55A10 now .....   Covering spaces, brachend coverings
1970 55A15 now .....   Graphs and map coloring
1970 55A20 now .....   Two-dimensional complexes
1970 55A25 now .....   Knots and links
1970 55A30 now .....   Wild knots and surfaces, etc.
1970 55A35 now .....   Dehn's Lemma, sphere theorem, loop theorem, aspherity
1970 55A40 now .....   Characterization of E3 and S3 (Poincare conjecture)
1970 55A99 now .....   None of the above, but in this section
1970 55Bxx now 55Nxx   Homology and cohomology theories
1970 55B05 now 55N05   Cech types
1970 55B10 now 55N10   Singular theory
1970 55B15 now 55N15   $K$-theory
1970 55B20 now 55N20   Generalized (extraordinary) homology and cohomology theories
1970 55B25 now 55N25   Homology with local coefficients, equivariant cohomology
1970 55B30 now 55N30   Sheaf cohomology
1970 55B35 now 55N35   Other homology theories
1970 55B40 now 55N40   Axioms for homology theory and uniqueness theorems
1970 55B45 now 55N45   Products and intersections
1970 55B99 now 55N99   None of the above, but in this section
1970 55Cxx now 55Mxx   Classical topics
1970 55C05 now 55M05   Duality
1970 55C10 now 55M10   Dimension theory
1970 55C15 now 55M15   Absolute neighborhood retracts
1970 55C20 now 55M20   Fixed points and coincidences
1970 55C25 now 55M25   Degree
1970 55C30 now 55M30   Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
1970 55C35 now 55M35   Finite groups of transformations (including Smith theory)
1970 55C99 now 55M99   None of the above, but in this section
1970 55Dxx now 55Pxx   Homotopy theory
1970 55D05 now 55P05   Homotopy extension properties, cofibrations
1970 55D10 now 55P10   Homotopy equivalences
1970 55D15 now 55P15   Classification of homotopy type
1970 55D20 now 55P20   Eilenberg-Mac Lane spaces
1970 55D25 now 55P25   Spanier-Whitehead duality
1970 55D30 now 55P30   Eckmann-Hilton duality
1970 55D35 now 55P35   Loop spaces
1970 55D40 now 55P40   Suspensions
1970 55D45 now 55P35   H-spaces and duals
1970 55D50 now 55M30   Category and cocategory, etc
1970 55D99 now 55P99   None of the above, but in this section
1970 55Exx now 55Qxx   Homotopy groups
1970 55E05 now 55Q05   Homotopy groups, general; sets of homotopy classes
1970 55E10 now 55Q10   Stable homotopy groups
1970 55E15 now 55Q15   Whitehead products and generalizations
1970 55E20 now 55Q20   Homotopy groups of wedges, joins, and simple spaces
1970 55E25 now 55Q25   Hopf invariants
1970 55E30 now 55Q05   Homotopy groups of triads, $n$-ads
1970 55E35 now 55Q35   Operations in homotopy groups
1970 55E40 now 55Q40   Homotopy groups of spheres
1970 55E45 now 55Q45   Stable homotopy of spheres
1970 55E50 now 55Q50   $J$-morphism
1970 55E55 now 55Q55   Cohomotopy groups
1970 55E99 now 55Q99   None of the above, but in this section
1970 55Fxx now 55Rxx   Fiber spaces and bundles
1970 55F05 now 55R05   Fiber spaces
1970 55F10 now 55R10   Fiber bundles
1970 55F15 now 55R15   Classification
1970 55F20 now 55R20   Spectral sequences and homology of fiber spaces
1970 55F25 now 55R25   Sphere bundles and vector space bundles
1970 55F35 now 55R35   Classifying spaces of groups and $H$-spaces
1970 55F40 now 55R40   Homology of classifying spaces, characteristic classes
1970 55F45 now 55R45   Homology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity
1970 55F50 now 55R50   Stable classes of vector space bundles, $K$-theory
1970 55F55 now 55R55   Fiberings with singularities
1970 55F60 now 55R60   Microbundles and block bundles
1970 55F65 now 55R65   Generalizations of fiber spaces and bundles
1970 55F99 now 55R99   None of the above, but in this section
1970 55Gxx now 55Sxx   Operations and obstructions
1970 55G05 now 55S05   Primary cohomology operations
1970 55G10 now 55S10   Steenrod algebra
1970 55G15 now 55S15   Symmetric products, cyclic products
1970 55G20 now 55S20   Secondary and higher cohomology operations
1970 55G25 now 55S25   $K$-theory operations and generalized cohomology operations
1970 55G30 now 55S30   Massey products
1970 55G35 now 55S35   Obstruction theory
1970 55G36 now 55S36   Extension and compression of mappings
1970 55G37 now 55S37   Classification of mappings
1970 55G40 now 55S40   Sectioning fiber spaces and bundles
1970 55G45 now 55S45   Postnikov systems, $k$-invariants
1970 55G99 now 55S99   None of the above, but in this section
1970 55Hxx now 55Txx   Spectral sequences
1970 55H05 now 55T05   General
1970 55H10 now 55T10   Serre spectral sequences
1970 55H15 now 55T15   Adams spectral sequences
1970 55H20 now 55T20   Eilenberg-Moore spectral sequences
1970 55H25 now 55T25   Generalized cohomology
1970 55H99 now 55T99   None of the above, but in this section
1970 55Jxx now 55Uxx   Applied homological algebra
1970 55J05 now 55U05   Abstract complexes
1970 55J10 now 55U10   Semisimplicial complexes
1970 55J15 now 55U15   Chain complexes
1970 55J20 now 55U20   Universal coefficient theorems, Bockstein operator
1970 55J25 now 55U25   Homology of a product, Künneth formula
1970 55J30 now 55U30   Duality
1970 55J99 now 55U99   None of the above, but in this section
    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]
1991 55P50 now 55M30   Category and cocategory, etc
    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
1991 55Q30 now 55Q05   Homotopy groups of triads, $n$-ads
    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 + 1991 + 1970