| 57-XX | | Prev: 55 | Up: Top | Next: 58 | |
| Manifolds and cell complexes [xref: 51H20] | |
| {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
[xref: 57N10]
| 57M05 |
Fundamental group, presentations, free differential calculus
[xref: 20F06, 20F34]
| 57M07 |
Topological methods in group theory
| 57M10 |
Covering spaces
| 57M12 |
Special coverings, e.g. branched
| 57M15 |
Relations with graph theory [See also 05Cxx]
[xref: 05C10]
| 57M20 |
Two-dimensional complexes
| 57M25 |
Knots and links in $S^3$ {For higher dimensions, see 57Q45}
[xref: 05C10, 32S55]
| 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 $E^3$ and $S^3$ (Poincaré conjecture) [See also 57N12]
[xref: 57N12]
| 57M50 |
Geometric structures on low-dimensional manifolds
[xref: 57N16]
| 57M60 |
Group actions in low dimensions
| 57M99 |
None of the above, but in this section
| |
57Nxx
| Topological manifolds
| 57N05 |
Topology of $E^2$, $2$-manifolds
| 57N10 |
Topology of general $3$-manifolds [See also 57Mxx]
| 57N12 |
Topology of $E^3$ and $S^3$ [See also 57M40]
[xref: 57M40]
| 57N13 |
Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx]
| 57N15 |
Topology of $E^n$, $n$-manifolds ($4 < n < \infty$)
| 57N16 |
Geometric structures on manifolds [See also 57M50]
| 57N17 |
Topology of topological vector spaces
| 57N20 |
Topology of infinite-dimensional manifolds [See also 58Bxx]
[xref: 46T05]
| 57N25 |
Shapes [See also 54C56, 55P55, 55Q07]
[xref: 54C56]
| 57N30 |
Engulfing
| 57N35 |
Embeddings and immersions
| 57N37 |
Isotopy and pseudo-isotopy
| 57N40 |
Neighborhoods of submanifolds
| 57N45 |
Flatness and tameness
| 57N50 |
$S^{n-1}\subset E^n$, Schoenflies problem
| 57N55 |
Microbundles and block bundles [See also 55R60, 57Q50]
[xref: 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]
[xref: 18F15]
| 57P05 |
Local properties of generalized manifolds
| 57P10 |
Poincaré 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]
[xref: 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}
[xref: 32S55]
| 57Q50 |
Microbundles and block bundles [See also 55R60, 57N55]
[xref: 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}
[xref: 53D35]
| 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
[xref: 55R40, 55Rxx]
| 57R22 |
Topology of vector bundles and fiber bundles [See also 55Rxx]
[xref: 55Rxx]
| 57R25 |
Vector fields, frame fields
[xref: 55Rxx]
| 57R27 |
Controllability of vector fields on $C^\infty$ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]
| 57R30 |
Foliations; geometric theory
[xref: 53C12]
| 57R32 |
Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
[xref: 22E41, 53C12, 58H10]
| 57R35 |
Differentiable mappings
| 57R40 |
Embeddings
[xref: 53C42]
| 57R42 |
Immersions
[xref: 53C42]
| 57R45 |
Singularities of differentiable mappings
| 57R50 |
Diffeomorphisms
| 57R52 |
Isotopy
| 57R55 |
Differentiable structures
| 57R56 |
Topological quantum field theories
[xref: 81T45]
| 57R57 |
Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
| 57R58 |
Floer homology
| 57R60 |
Homotopy spheres, Poincaré conjecture
| 57R65 |
Surgery and handlebodies
[xref: 18F25]
| 57R67 |
Surgery obstructions, Wall groups [See also 19J25]
[xref: 18F25, 19J25]
| 57R70 |
Critical points and critical submanifolds
| 57R75 |
O- and SO-cobordism
[xref: 55N22]
| 57R77 |
Complex cobordism (U- and SU-cobordism) [See also 55N22]
[xref: 55N22]
| 57R80 |
$h$- and $s$-cobordism
| 57R85 |
Equivariant cobordism
[xref: 55N22]
| 57R90 |
Other types of cobordism [See also 55N22]
[xref: 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, 37-XX, 54H15, 58D05]
[xref: 20F34, 54H15]
| 57S05 |
Topological properties of groups of homeomorphisms or diffeomorphisms
[xref: 58D05]
| 57S10 |
Compact groups of homeomorphisms
| 57S15 |
Compact Lie groups of differentiable transformations
| 57S17 |
Finite transformation groups
[xref: 55M35]
| 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
[xref: 18Gxx, 22E41, 55Nxx, 55R40]
| 57T05 |
Hopf algebras [See also 16W30]
[xref: 16W30]
| 57T10 |
Homology and cohomology of Lie groups
| 57T15 |
Homology and cohomology of homogeneous spaces of Lie groups
[xref: 14M17, 32M10, 32M15, 53C30, 53C35]
| 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]
[xref: 55T20]
| 57T99 |
None of the above, but in this section
| |