ID:2000 55-XX 1+. CT:Algebraic topology ZZ:---------- ID:2000 55-00 3+. CN:General reference works (handbooks, dictionaries, bibliographies, etc.) ZZ:---------- ID:2000 55-01 3+. CN:Instructional exposition (textbooks, tutorial papers, etc.) ZZ:---------- ID:2000 55-02 3+. CN:Research exposition (monographs, survey articles) ZZ:---------- ID:2000 55-03 3+. CN:Historical (must also be assigned at least one classification number from Section 01) ZZ:---------- ID:2000 55-04 3-. CN:Explicit machine computation and programs (not the theory of computation or programming) ZZ:---------- ID:2000 55-06 3+. CN:Proceedings, conferences, collections, etc. ZZ:---------- ID:1970 55Axx 2+. now ..... CN:Low-dimensional topology ZZ:---------- ID:1970 55A05 3+. now ..... CN:Fundamental group, presentation, free differential calculus ZZ:---------- ID:1970 55A10 3+. now ..... CN:Covering spaces, brachend coverings ZZ:---------- ID:1970 55A15 3+. now ..... CN:Graphs and map coloring ZZ:---------- ID:1970 55A20 3+. now ..... CN:Two-dimensional complexes ZZ:---------- ID:1970 55A25 3+. now ..... CN:Knots and links ZZ:---------- ID:1970 55A30 3+. now ..... CN:Wild knots and surfaces, etc. ZZ:---------- ID:1970 55A35 3+. now ..... CN:Dehn's Lemma, sphere theorem, loop theorem, aspherity ZZ:---------- ID:1970 55A40 3+. now ..... CN:Characterization of E3 and S3 (Poincare conjecture) ZZ:---------- ID:1970 55A99 3+. now ..... CN:None of the above, but in this section ZZ:---------- ID:1970 55Bxx 2+. now 55Nxx CN:Homology and cohomology theories ZZ:---------- ID:1970 55B05 3+. now 55N05 CN:Cech types ZZ:---------- ID:1970 55B10 3+. now 55N10 CN:Singular theory ZZ:---------- ID:1970 55B15 3+. now 55N15 CN:$K$-theory ZZ:---------- ID:1970 55B20 3+. now 55N20 CN:Generalized (extraordinary) homology and cohomology theories ZZ:---------- ID:1970 55B25 3+. now 55N25 CN:Homology with local coefficients, equivariant cohomology ZZ:---------- ID:1970 55B30 3+. now 55N30 CN:Sheaf cohomology ZZ:---------- ID:1970 55B35 3+. now 55N35 CN:Other homology theories ZZ:---------- ID:1970 55B40 3+. now 55N40 CN:Axioms for homology theory and uniqueness theorems ZZ:---------- ID:1970 55B45 3+. now 55N45 CN:Products and intersections ZZ:---------- ID:1970 55B99 3+. now 55N99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Cxx 2+. now 55Mxx CN:Classical topics ZZ:---------- ID:1970 55C05 3+. now 55M05 CN:Duality ZZ:---------- ID:1970 55C10 3+. now 55M10 CN:Dimension theory ZZ:---------- ID:1970 55C15 3+. now 55M15 CN:Absolute neighborhood retracts ZZ:---------- ID:1970 55C20 3+. now 55M20 CN:Fixed points and coincidences ZZ:---------- ID:1970 55C25 3+. now 55M25 CN:Degree ZZ:---------- ID:1970 55C30 3+. now 55M30 CN:Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space ZZ:---------- ID:1970 55C35 3+. now 55M35 CN:Finite groups of transformations (including Smith theory) ZZ:---------- ID:1970 55C99 3+. now 55M99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Dxx 2+. now 55Pxx CN:Homotopy theory ZZ:---------- ID:1970 55D05 3+. now 55P05 CN:Homotopy extension properties, cofibrations ZZ:---------- ID:1970 55D10 3+. now 55P10 CN:Homotopy equivalences ZZ:---------- ID:1970 55D15 3+. now 55P15 CN:Classification of homotopy type ZZ:---------- ID:1970 55D20 3+. now 55P20 CN:Eilenberg-Mac Lane spaces ZZ:---------- ID:1970 55D25 3+. now 55P25 CN:Spanier-Whitehead duality ZZ:---------- ID:1970 55D30 3+. now 55P30 CN:Eckmann-Hilton duality ZZ:---------- ID:1970 55D35 3+. now 55P35 CN:Loop spaces ZZ:---------- ID:1970 55D40 3+. now 55P40 CN:Suspensions ZZ:---------- ID:1970 55D45 3+. now 55P35 CN:H-spaces and duals ZZ:---------- ID:1970 55D50 3+. now 55M30 CN:Category and cocategory, etc ZZ:---------- ID:1970 55D99 3+. now 55P99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Exx 2+. now 55Qxx CN:Homotopy groups ZZ:---------- ID:1970 55E05 3+. now 55Q05 CN:Homotopy groups, general; sets of homotopy classes ZZ:---------- ID:1970 55E10 3+. now 55Q10 CN:Stable homotopy groups ZZ:---------- ID:1970 55E15 3+. now 55Q15 CN:Whitehead products and generalizations ZZ:---------- ID:1970 55E20 3+. now 55Q20 CN:Homotopy groups of wedges, joins, and simple spaces ZZ:---------- ID:1970 55E25 3+. now 55Q25 CN:Hopf invariants ZZ:---------- ID:1970 55E30 3+. now 55Q05 CN:Homotopy groups of triads, $n$-ads ZZ:---------- ID:1970 55E35 3+. now 55Q35 CN:Operations in homotopy groups ZZ:---------- ID:1970 55E40 3+. now 55Q40 CN:Homotopy groups of spheres ZZ:---------- ID:1970 55E45 3+. now 55Q45 CN:Stable homotopy of spheres ZZ:---------- ID:1970 55E50 3+. now 55Q50 CN:$J$-morphism ZZ:---------- ID:1970 55E55 3+. now 55Q55 CN:Cohomotopy groups ZZ:---------- ID:1970 55E99 3+. now 55Q99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Fxx 2+. now 55Rxx CN:Fiber spaces and bundles ZZ:---------- ID:1970 55F05 3+. now 55R05 CN:Fiber spaces ZZ:---------- ID:1970 55F10 3+. now 55R10 CN:Fiber bundles ZZ:---------- ID:1970 55F15 3+. now 55R15 CN:Classification ZZ:---------- ID:1970 55F20 3+. now 55R20 CN:Spectral sequences and homology of fiber spaces ZZ:---------- ID:1970 55F25 3+. now 55R25 CN:Sphere bundles and vector space bundles ZZ:---------- ID:1970 55F35 3+. now 55R35 CN:Classifying spaces of groups and $H$-spaces ZZ:---------- ID:1970 55F40 3+. now 55R40 CN:Homology of classifying spaces, characteristic classes ZZ:---------- ID:1970 55F45 3+. now 55R45 CN:Homology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity ZZ:---------- ID:1970 55F50 3+. now 55R50 CN:Stable classes of vector space bundles, $K$-theory ZZ:---------- ID:1970 55F55 3+. now 55R55 CN:Fiberings with singularities ZZ:---------- ID:1970 55F60 3+. now 55R60 CN:Microbundles and block bundles ZZ:---------- ID:1970 55F65 3+. now 55R65 CN:Generalizations of fiber spaces and bundles ZZ:---------- ID:1970 55F99 3+. now 55R99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Gxx 2+. now 55Sxx CN:Operations and obstructions ZZ:---------- ID:1970 55G05 3+. now 55S05 CN:Primary cohomology operations ZZ:---------- ID:1970 55G10 3+. now 55S10 CN:Steenrod algebra ZZ:---------- ID:1970 55G15 3+. now 55S15 CN:Symmetric products, cyclic products ZZ:---------- ID:1970 55G20 3+. now 55S20 CN:Secondary and higher cohomology operations ZZ:---------- ID:1970 55G25 3+. now 55S25 CN:$K$-theory operations and generalized cohomology operations ZZ:---------- ID:1970 55G30 3+. now 55S30 CN:Massey products ZZ:---------- ID:1970 55G35 3+. now 55S35 CN:Obstruction theory ZZ:---------- ID:1970 55G36 3+. now 55S36 CN:Extension and compression of mappings ZZ:---------- ID:1970 55G37 3+. now 55S37 CN:Classification of mappings ZZ:---------- ID:1970 55G40 3+. now 55S40 CN:Sectioning fiber spaces and bundles ZZ:---------- ID:1970 55G45 3+. now 55S45 CN:Postnikov systems, $k$-invariants ZZ:---------- ID:1970 55G99 3+. now 55S99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Hxx 2+. now 55Txx CN:Spectral sequences ZZ:---------- ID:1970 55H05 3+. now 55T05 CN:General ZZ:---------- ID:1970 55H10 3+. now 55T10 CN:Serre spectral sequences ZZ:---------- ID:1970 55H15 3+. now 55T15 CN:Adams spectral sequences ZZ:---------- ID:1970 55H20 3+. now 55T20 CN:Eilenberg-Moore spectral sequences ZZ:---------- ID:1970 55H25 3+. now 55T25 CN:Generalized cohomology ZZ:---------- ID:1970 55H99 3+. now 55T99 CN:None of the above, but in this section ZZ:---------- ID:1970 55Jxx 2+. now 55Uxx CN:Applied homological algebra ZZ:---------- ID:1970 55J05 3+. now 55U05 CN:Abstract complexes ZZ:---------- ID:1970 55J10 3+. now 55U10 CN:Semisimplicial complexes ZZ:---------- ID:1970 55J15 3+. now 55U15 CN:Chain complexes ZZ:---------- ID:1970 55J20 3+. now 55U20 CN:Universal coefficient theorems, Bockstein operator ZZ:---------- ID:1970 55J25 3+. now 55U25 CN:Homology of a product, Künneth formula ZZ:---------- ID:1970 55J30 3+. now 55U30 CN:Duality ZZ:---------- ID:1970 55J99 3+. now 55U99 CN:None of the above, but in this section ZZ:---------- ID:2000 55Mxx 2+. CN:Classical topics VS:For the topology of Euclidean spaces and manifolds, see 57Nxx XR:54F35 ZZ:---------- ID:2000 55M05 3+. CN:Duality ZZ:---------- ID:2000 55M10 3+. CN:Dimension theory VW:See also 54F45 XR:54F45 ZZ:---------- ID:2000 55M15 3+. CN:Absolute neighborhood retracts VW:See also 54C55 XR:54C55 ZZ:---------- ID:2000 55M20 3+. CN:Fixed points and coincidences VW:See also 54H25 XR:47H10, 54H25 ZZ:---------- ID:2000 55M25 3+. CN:Degree, winding number XR:47H11 ZZ:---------- ID:2000 55M30 3-. CN:Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space ZZ:---------- ID:2000 55M35 3+. CN:Finite groups of transformations (including Smith theory) VW:See also 57S17 ZZ:---------- ID:2000 55M99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Nxx 2+. CN:Homology and cohomology theories VW:See also 57Txx XR:18Gxx, 54F35 ZZ:---------- ID:2000 55N05 3-. CN:Cech types XR:55Q70 ZZ:---------- ID:2000 55N07 3-. CN:Steenrod-Sitnikov homologies XR:55Q70 ZZ:---------- ID:2000 55N10 3+. CN:Singular theory ZZ:---------- ID:2000 55N15 3+. CN:$K$-theory VW:See also 19Lxx VS:For algebraic $K$-theory, see 18F25, 19-XX ZZ:---------- ID:2000 55N20 3+. CN:Generalized (extraordinary) homology and cohomology theories ZZ:---------- ID:2000 55N22 3+. CN:Bordism and cobordism theories, formal group laws VW:See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90 XR:14L05, 19K33, 19L41, 57R77, 57R90 ZZ:---------- ID:2000 55N25 3+. CN:Homology with local coefficients, equivariant cohomology ZZ:---------- ID:2000 55N30 3+. CN:Sheaf cohomology VW:See also 18F20, 32C35, 32L10 XR:18F20, 32C35, 32L10 ZZ:---------- ID:2000 55N33 3-. CN:Intersection homology and cohomology ZZ:---------- ID:2000 55N34 3-. CN:Elliptic cohomology ZZ:---------- ID:2000 55N35 3+. CN:Other homology theories ZZ:---------- ID:2000 55N40 3-. CN:Axioms for homology theory and uniqueness theorems ZZ:---------- ID:2000 55N45 3-. CN:Products and intersections ZZ:---------- ID:2000 55N91 3+. CN:Equivariant homology and cohomology VW:See also 19L47 XR:19L47 ZZ:---------- ID:2000 55N99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Pxx 2+. CN:Homotopy theory VS:For simple homotopy type, see 57Q10 ZZ:---------- ID:2000 55P05 3-. CN:Homotopy extension properties, cofibrations ZZ:---------- ID:2000 55P10 3+. CN:Homotopy equivalences ZZ:---------- ID:2000 55P15 3+. CN:Classification of homotopy type ZZ:---------- ID:2000 55P20 3-. CN:Eilenberg-Mac Lane spaces ZZ:---------- ID:2000 55P25 3-. CN:Spanier-Whitehead duality ZZ:---------- ID:2000 55P30 3-. CN:Eckmann-Hilton duality ZZ:---------- ID:2000 55P35 3+. CN:Loop spaces ZZ:---------- ID:2000 55P40 3-. CN:Suspensions ZZ:---------- ID:2000 55P42 3+. CN:Stable homotopy theory, spectra ZZ:---------- ID:2000 55P43 3-. CN:Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) ZZ:---------- ID:2000 55P45 3+. CN:$H$-spaces and duals ZZ:---------- ID:2000 55P47 3-. CN:Infinite loop spaces ZZ:---------- ID:2000 55P48 3-. CN:Loop space machines, operads VW:See also 18D50 XR:18D50 ZZ:---------- ID:1991 55P50 3+. now 55M30 CN:Category and cocategory, etc ZZ:---------- ID:2000 55P55 3+. CN:Shape theory VW:See also 54C56, 55Q07 XR:54C56, 57N25 ZZ:---------- ID:2000 55P57 3-. CN:Proper homotopy theory ZZ:---------- ID:2000 55P60 3-. CN:Localization and completion ZZ:---------- ID:2000 55P62 3-. CN:Rational homotopy theory ZZ:---------- ID:2000 55P65 3-. CN:Homotopy functors ZZ:---------- ID:2000 55P91 3+. CN:Equivariant homotopy theory VW:See also 19L47 XR:19L47 ZZ:---------- ID:2000 55P92 3-. CN:Relations between equivariant and nonequivariant homotopy theory ZZ:---------- ID:2000 55P99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Qxx 2+. CN:Homotopy groups ZZ:---------- ID:2000 55Q05 3-. CN:Homotopy groups, general; sets of homotopy classes ZZ:---------- ID:2000 55Q07 3-. CN:Shape groups XR:55P55, 57N25 ZZ:---------- ID:2000 55Q10 3-. CN:Stable homotopy groups ZZ:---------- ID:2000 55Q15 3-. CN:Whitehead products and generalizations ZZ:---------- ID:2000 55Q20 3-. CN:Homotopy groups of wedges, joins, and simple spaces ZZ:---------- ID:2000 55Q25 3-. CN:Hopf invariants ZZ:---------- ID:1991 55Q30 3+. now 55Q05 CN:Homotopy groups of triads, $n$-ads ZZ:---------- ID:2000 55Q35 3-. CN:Operations in homotopy groups ZZ:---------- ID:2000 55Q40 3-. CN:Homotopy groups of spheres ZZ:---------- ID:2000 55Q45 3+. CN:Stable homotopy of spheres ZZ:---------- ID:2000 55Q50 3+. CN:$J$-morphism VW:See also 19L20 XR:19L20 ZZ:---------- ID:2000 55Q51 3-. CN:$v_n$-periodicity ZZ:---------- ID:2000 55Q52 3-. CN:Homotopy groups of special spaces ZZ:---------- ID:2000 55Q55 3-. CN:Cohomotopy groups ZZ:---------- ID:2000 55Q70 3-. CN:Homotopy groups of special types VW:See also 55N05, 55N07 ZZ:---------- ID:2000 55Q91 3+. CN:Equivariant homotopy groups VW:See also 19L47 XR:19L47 ZZ:---------- ID:2000 55Q99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Rxx 2+. CN:Fiber spaces and bundles VW:See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25 XR:18F15, 32Lxx, 46L80, 46M20, 57R22 ZZ:---------- ID:2000 55R05 3+. CN:Fiber spaces ZZ:---------- ID:2000 55R10 3+. CN:Fiber bundles ZZ:---------- ID:2000 55R12 3-. CN:Transfer ZZ:---------- ID:2000 55R15 3-. CN:Classification ZZ:---------- ID:2000 55R20 3+. CN:Spectral sequences and homology of fiber spaces VW:See also 55Txx XR:55Txx, 57T35 ZZ:---------- ID:2000 55R25 3+. CN:Sphere bundles and vector bundles ZZ:---------- ID:2000 55R35 3+. CN:Classifying spaces of groups and $H$-spaces ZZ:---------- ID:2000 55R37 3-. CN:Maps between classifying spaces ZZ:---------- ID:2000 55R40 3+. CN:Homology of classifying spaces, characteristic classes VW:See also 57Txx, 57R20 ZZ:---------- ID:2000 55R45 3-. CN:Homology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity ZZ:---------- ID:2000 55R50 3+. CN:Stable classes of vector space bundles, $K$-theory VW:See also 19Lxx VS:For algebraic $K$-theory, see 18F25, 19-XX ZZ:---------- ID:2000 55R55 3-. CN:Fiberings with singularities ZZ:---------- ID:2000 55R60 3+. CN:Microbundles and block bundles VW:See also 57N55, 57Q50 XR:57N55, 57Q50 ZZ:---------- ID:2000 55R65 3-. CN:Generalizations of fiber spaces and bundles ZZ:---------- ID:2000 55R70 3-. CN:Fibrewise topology ZZ:---------- ID:2000 55R80 3-. CN:Discriminantal varieties, configuration spaces ZZ:---------- ID:2000 55R91 3+. CN:Equivariant fiber spaces and bundles VW:See also 19L47 XR:19L47 ZZ:---------- ID:2000 55R99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Sxx 2+. CN:Operations and obstructions ZZ:---------- ID:2000 55S05 3-. CN:Primary cohomology operations ZZ:---------- ID:2000 55S10 3+. CN:Steenrod algebra ZZ:---------- ID:2000 55S12 3-. CN:Dyer-Lashof operations ZZ:---------- ID:2000 55S15 3-. CN:Symmetric products, cyclic products ZZ:---------- ID:2000 55S20 3-. CN:Secondary and higher cohomology operations ZZ:---------- ID:2000 55S25 3+. CN:$K$-theory operations and generalized cohomology operations VW:See also 19D55, 19Lxx ZZ:---------- ID:2000 55S30 3+. CN:Massey products ZZ:---------- ID:2000 55S35 3+. CN:Obstruction theory ZZ:---------- ID:2000 55S36 3-. CN:Extension and compression of mappings ZZ:---------- ID:2000 55S37 3-. CN:Classification of mappings ZZ:---------- ID:2000 55S40 3-. CN:Sectioning fiber spaces and bundles ZZ:---------- ID:2000 55S45 3+. CN:Postnikov systems, $k$-invariants ZZ:---------- ID:2000 55S91 3+. CN:Equivariant operations and obstructions VW:See also 19L47 XR:19L47 ZZ:---------- ID:2000 55S99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Txx 2+. CN:Spectral sequences VW:See also 18G40, 55R20 XR:18G40, 55R20 ZZ:---------- ID:2000 55T05 3-. CN:General ZZ:---------- ID:2000 55T10 3+. CN:Serre spectral sequences ZZ:---------- ID:2000 55T15 3+. CN:Adams spectral sequences ZZ:---------- ID:2000 55T20 3+. CN:Eilenberg-Moore spectral sequences VW:See also 57T35 XR:57T35 ZZ:---------- ID:2000 55T25 3+. CN:Generalized cohomology ZZ:---------- ID:2000 55T99 3-. CN:None of the above, but in this section ZZ:---------- ID:2000 55Uxx 2+. CN:Applied homological algebra and category theory VW:See also 18Gxx XR:18Gxx, 57T30 ZZ:---------- ID:2000 55U05 3-. CN:Abstract complexes ZZ:---------- ID:2000 55U10 3-. CN:Simplicial sets and complexes XR:13F55, 18G30 ZZ:---------- ID:2000 55U15 3-. CN:Chain complexes ZZ:---------- ID:2000 55U20 3-. CN:Universal coefficient theorems, Bockstein operator ZZ:---------- ID:2000 55U25 3-. CN:Homology of a product, Künneth formula XR:18G15 ZZ:---------- ID:2000 55U30 3-. CN:Duality ZZ:---------- ID:2000 55U35 3+. CN:Abstract and axiomatic homotopy theory ZZ:---------- ID:2000 55U40 3-. CN:Topological categories, foundations of homotopy theory ZZ:---------- ID:2000 55U99 3+. CN:None of the above, but in this section ZZ:----------