55R50 Stable classes of vector space bundles, $K$-theory [See also <a href="#code:19Lxx">19Lxx</a>] {For algebraic $K$-theory, see <a href="#code:18F25">18F25</a>, <a href="#code:19-XX">19-XX</a>}

55R60 Microbundles and block bundles [See also <a href="#code:57N55">57N55</a>, <a href="#code:57Q50">57Q50</a>]

55R65 Generalizations of fiber spaces and bundles

55R80 Discriminantal varieties, configuration spaces

55R91 Equivariant fiber spaces and bundles [See also <a href="#code:19L47">19L47</a>]

55R99 None of the above, but in this section

55S15 Symmetric products, cyclic products

55S20 Secondary and higher cohomology operations

55S25 $K$-theory operations and generalized cohomology operations [See also <a href="#code:19D55">19D55</a>, <a href="#code:19Lxx">19Lxx</a>]

55S36 Extension and compression of mappings

55S40 Sectioning fiber spaces and bundles

55S91 Equivariant operations and obstructions [See also <a href="#code:19L47">19L47</a>]

55S99 None of the above, but in this section

55Txx Spectral sequences [See also <a href="#code:18G40">18G40</a>, <a href="#code:55R20">55R20</a>]

55T20 Eilenberg-Moore spectral sequences [See also <a href="#code:57T35">57T35</a>]

55T99 None of the above, but in this section

55Uxx Applied homological algebra and category theory [See also <a href="#code:18Gxx">18Gxx</a>]

55U20 Universal coefficient theorems, Bockstein operator

55U25 Homology of a product, Künneth formula

55U35 Abstract and axiomatic homotopy theory

55U40 Topological categories, foundations of homotopy theory

55U99 None of the above, but in this section

57-XX Manifolds and cell complexes {For complex manifolds, see <a href="#code:32Qxx">32Qxx</a>}

57-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

57-01 Instructional exposition (textbooks, tutorial papers, etc.)

57-02 Research exposition (monographs, survey articles)

57-03 Historical (must also be assigned at least one classification number from Section 01)

57-04 Explicit machine computation and programs (not the theory of computation or programming)