55Nxx Homology and cohomology theories [See also 57Txx]
 55N05 Cech types
 55N07 SteenrodSitnikov homologies
 55N10 Singular theory
 55N15 Ktheory [See also 19Lxx] (For algebraic Ktheory, see 18F25, 19 XXg 55N20 Generalized (extraordinary) homology and cohomology theories

55N22 Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]
(1)
 55N25 Homology with local coefficients, equivariant cohomology
 55N30 Sheaf cohomology [See also 18F20, 32C35, 32L10]
 55N32 Orbifold cohomology
 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]
 55N99 None of the above, but in this section