57-XX	Manifolds and cell complexes {For complex manifolds, see 32Qxx}
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)
57-06	Proceedings, conferences, collections, etc.
57Mxx	Low-dimensional topology
57M05	Fundamental group, presentations, free differential calculus
57M07	Topological methods in group theory
57M10	Covering spaces
57M12	Special coverings, e.g. Branched
57M15	Relations with graph theory [See also 05Cxx]
57M20	Two-dimensional complexes
57M25	Knots and links in S3 {For higher dimensions, see 57Q45}
57M27	Invariants of knots and 3-manifolds
57M30	Wild knots and surfaces, etc., wild embeddings
57M35	Dehn's lemma, sphere theorem, loop theorem, asphericity
57M40	Characterizations of E3 and S3 (Poincar\'e conjecture) [See also 57N12]
57M50	Geometric structures on low-dimensional manifolds
57M60	Group actions in low dimensions
57M99	None of the above, but in this section
57Nxx	Topological manifolds
57N05	Topology of E2, 2-manifolds
57N10	Topology of general 3-manifolds [See also 57Mxx]
57N12	Topology of E3 and S3 [See also 57M40]
57N13	Topology of E4, 4-manifolds [See also 14Jxx, 32Jxx]
57N15	Topology of En, n-manifolds (4n\infty)
57N16	Geometric structures on manifolds [See also 57M50]
57N17	Topology of topological vector spaces
57N20	Topology of infinite-dimensional manifolds [See also 58Bxx]
57N25	Shapes [See also 54C56, 55P55, 55Q07]
57N30	Engulfing
57N35	Embeddings and immersions
57N37	Isotopy and pseudo-isotopy
57N40	Neighborhoods of submanifolds
57N45	Flatness and tameness
57N50	Sn-1\subsetEn, Schoenflies problem
57N55	Microbundles and block bundles [See also 55R60, 57Q50]
57N60	Cellularity
57N65	Algebraic topology of manifolds
57N70	Cobordism and concordance
57N75	General position and transversality
57N80	Stratifications
57N99	None of the above, but in this section
57Pxx	Generalized manifolds [See also 18F15]
57P05	Local properties of generalized manifolds
57P10	Poincar\'e duality spaces
57P99	None of the above, but in this section
57Qxx	PL-topology
57Q05	General topology of complexes
57Q10	Simple homotopy type, Whitehead torsion, Reidemeister - Franz torsion, etc. [See also 19B28]
57Q12	Wall finiteness obstruction for CW-complexes
57Q15	Triangulating manifolds
57Q20	Cobordism
57Q25	Comparison of PL-structures: classification, Hauptvermutung
57Q30	Engulfing
57Q35	Embeddings and immersions
57Q37	Isotopy
57Q40	Regular neighborhoods
57Q45	Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
57Q50	Microbundles and block bundles [See also 55R60, 57N55]
57Q55	Approximations
57Q60	Cobordism and concordance
57Q65	General position and transversality
57Q91	Equivariant PL-topology
57Q99	None of the above, but in this section
57Rxx	Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}
57R05	Triangulating
57R10	Smoothing
57R12	Smooth approximations
57R15	Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57R17	Symplectic and contact topology
57R19	Algebraic topology on manifolds
57R20	Characteristic classes and numbers
57R22	Topology of vector bundles and fiber bundles [See also 55Rxx]
57R25	Vector fields, frame fields
57R27	Controllability of vector fields on Cinfty and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]
57R30	Foliations; geometric theory
57R32	Classifying spaces for foliations; Gelfand - Fuks cohomology [See also 58H10]
57R35	Differentiable mappings
57R40	Embeddings
57R42	Immersions
57R45	Singularities of differentiable mappings
57R50	Diffeomorphisms
57R52	Isotopy
57R55	Differentiable structures
57R56	Topological quantum field theories
57R57	Applications of global analysis to structures on manifolds, Donaldson and Seiberg - Witten invariants [See also 58-XX]
57R58	Floer homology
57R60	Homotopy spheres, Poincar\'e conjecture
57R65	Surgery and handlebodies
57R67	Surgery obstructions, Wall groups [See also 19J25]
57R70	Critical points and critical submanifolds
57R75	O- and SO-cobordism
57R77	Complex cobordism (U- and SU-cobordism) [See also 55N22]
57R80	h- and s-cobordism
57R85	Equivariant cobordism
57R90	Other types of cobordism [See also 55N22]
57R91	Equivariant algebraic topology of manifolds
57R95	Realizing cycles by submanifolds
57R99	None of the above, but in this section
57Sxx	Topological transformation groups [See also 20F34, 22-XX, 54H15, 58D05]
57S05	Topological properties of groups of homeomorphisms or diffeomorphisms
57S10	Compact groups of homeomorphisms
57S15	Compact Lie groups of differentiable transformations
57S17	Finite transformation groups
57S20	Noncompact Lie groups of transformations
57S25	Groups acting on specific manifolds
57S30	Discontinuous groups of transformations
57S99	None of the above, but in this section
57Txx	Homology and homotopy of topological groups and related structures
57T05	Hopf algebras [See also 16W30]
57T10	Homology and cohomology of Lie groups
57T15	Homology and cohomology of homogeneous spaces of Lie groups
57T20	Homotopy groups of topological groups and homogeneous spaces
57T25	Homology and cohomology of H-spaces
57T30	Bar and cobar constructions [See also 18G55, 55Uxx]
57T35	Applications of Eilenberg - Moore spectral sequences [See also 55R20, 55T20]
57T99	None of the above, but in this section