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Mathematics Subject Classification 1991
57-XX Manifolds and cell complexes, {For complex manifolds, See 32C10}
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57-00
General reference works (handbooks, dictionaries, bibliographies, etc.)
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57-01
Instructional exposition (textbooks, tutorial papers, etc.)
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57-02
Research exposition (monographs, survey articles)
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57-03
Historical (must be assigned at least one classification number from Section 01)
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57-04
Explicit machine computation and programs (not the theory of computation or programming)
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57-06
Proceedings, conferences, collections, etc.
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57Mxx Low-dimensional topology
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57M05
Fundamental group, presentations, free differential calculus
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57M07
Topological methods in group theory
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57M10
Covering spaces
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57M12
Special coverings, e.g. branched
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57M15
Relations with graph theory, See also {05Cxx}
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57M20
Two-dimensional complexes
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57M25
Knots and links in $S^3$, {For higher dimensions, See 57Q45}
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57M30
Wild knots and surfaces, etc., wild embeddings
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57M35
Dehn's lemma, sphere theorem, loop theorem, asphericity
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57M40
Characterizations of $E^3$ and $S^3$ (Poincare conjecture), See also {57N12}
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57M50
Geometric structures on low-dimensional manifolds
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57M60
Group actions in low dimensions
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57M99
None of the above but in this section
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57Nxx Topological manifolds
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57N05
Topology of $E^2$, $2$-manifolds
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57N10
Topology of general $3$-manifolds, See also {57Mxx}
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57N12
Topology of $E^3$ and $S^3$, See also {57M40}
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57N13
Topology of $E^4$, $4$-manifolds, See also {14Jxx, 32Jxx}
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57N15
Topology of $E^n$, $n$-manifolds ($4 less n less infty$)
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57N17
Topology of topological vector spaces
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57N20
Topology of infinite-dimensional manifolds, See Also { 58Bxx}
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57N25
Shapes, See also {54C56, 55P55, 55Q07}
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57N30
Engulfing
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57N35
Embeddings and immersions
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57N37
Isotopy and pseudo-isotopy
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57N40
Neighborhoods of submanifolds
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57N45
Flatness and tameness
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57N50
$S^{n-1}subset E^n$, Schoenflies problem
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57N55
Microbundles and block bundles, See also {55R60, 57Q50}
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57N60
Cellularity
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57N65
Algebraic topology of manifolds
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57N70
Cobordism and concordance
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57N75
General position and transversality
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57N80
Stratifications
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57N99
None of the above but in this section
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57Pxx Generalized manifolds, See also {18F15}
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57P05
Local properties of generalized manifolds
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57P10
Poincare duality spaces
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57P99
None of the above but in this section
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57Qxx PL-topology
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57Q05
General topology of complexes
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57Q10
Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc., See also {19B28}
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57Q12
Wall finiteness obstruction for CW-complexes
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57Q15
Triangulating manifolds
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57Q20
Cobordism
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57Q25
Comparison of PL-structures: classification, Hauptvermutung
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57Q30
Engulfing
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57Q35
Embeddings and immersions
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57Q37
Isotopy
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57Q40
Regular neighborhoods
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57Q45
Knots and links (in high dimensions), {For the low-dimensional case, See 57M25}
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57Q50
Microbundles and block bundles, See also {55R60, 57N55}
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57Q55
Approximations
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57Q60
Cobordism and concordance
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57Q65
General position and transversality
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57Q91
Equivariant PL-topology
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57Q99
None of the above but in this section
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57Rxx Differential topology, {For foundational questions of differentiable manifolds, See 58Axx; for infinite-dimensional manifolds, See 58Bxx}
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57R05
Triangulating
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57R10
Smoothing
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57R12
Smooth approximations
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57R15
Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
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57R19
Algebraic topology on manifolds
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57R20
Characteristic classes and numbers
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57R22
Topology of vector bundles and fiber bundles, See Also {55Rxx}
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57R25
Vector fields, frame fields
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57R27
Controllability of vector fields on $C^infty$ and real-analytic manifolds, See also {49Qxx, 58F40, 93B05}
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57R30
Foliations; geometric theory
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57R32
Classifying spaces for foliations; Gelfand-Fuks cohomology, See also {58H10}
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57R35
Differentiable mappings
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57R40
Embeddings
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57R42
Immersions
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57R45
Singularities of differentiable mappings
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57R50
Diffeomorphisms
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57R52
Isotopy
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57R55
Differentiable structures
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57R57
Applications of global analysis to structures on manifolds, See also {58-XX}
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57R60
Homotopy spheres, Poincare conjecture
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57R65
Surgery and handlebodies
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57R67
Surgery obstructions, Wall groups, See also {19J25}
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57R70
Critical points and critical submanifolds
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57R75
O- and SO-cobordism
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57R77
Complex cobordism (U- and SU-cobordism), See also {55N22}
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57R80
$h$- and $s$-cobordism
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57R85
Equivariant cobordism
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57R90
Other types of cobordism See{55N22}
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57R91
Equivariant algebraic topology of manifolds
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57R95
Realizing cycles by submanifolds
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57R99
None of the above but in this section
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57Sxx Topological transformation groups, See also {20F34, 22-XX, 54H15, 58D05}
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57S05
Topological properties of groups of homeomorphisms or diffeomorphisms
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57S10
Compact groups of homeomorphisms
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57S15
Compact Lie groups of differentiable transformations
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57S17
Finite transformation groups
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57S20
Noncompact Lie groups of transformations
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57S25
Groups acting on specific manifolds
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57S30
Discontinuous groups of transformations
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57S99
None of the above but in this section
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57Txx Homology and homotopy of topological groups and related structures
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57T05
Hopf algebras, See also {16W30}
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57T10
Homology and cohomology of Lie groups
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57T15
Homology and cohomology of homogeneous spaces of Lie groups
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57T20
Homotopy groups of topological groups and homogeneous spaces
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57T25
Homology and cohomology of ${H}$-spaces
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57T30
Bar and cobar constructions, See also {18G55, 55Uxx}
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57T35
Applications of Eilenberg-Moore spectral sequences, See also {55R20, 55T20}
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57T99
None of the above but in this section
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Letzte Änderung: 10. Nov. 2010