Mathematics Subject Classification 1991

57-XX Manifolds and cell complexes, {For complex manifolds, See 32C10} ( 0 Dok.)

• 57-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 57-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 57-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 57-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 57-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 57-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 57Mxx Low-dimensional topology ( 0 Dok. )
• 57M05 Fundamental group, presentations, free differential calculus ( 0 Dok.)
• 57M07 Topological methods in group theory ( 0 Dok.)
• 57M10 Covering spaces ( 0 Dok.)
• 57M12 Special coverings, e.g. branched ( 0 Dok.)
• 57M15 Relations with graph theory, See also {05Cxx} ( 0 Dok.)
• 57M20 Two-dimensional complexes ( 0 Dok.)
• 57M25 Knots and links in $S^3$, {For higher dimensions, See 57Q45} ( 0 Dok.)
• 57M30 Wild knots and surfaces, etc., wild embeddings ( 0 Dok.)
• 57M35 Dehn's lemma, sphere theorem, loop theorem, asphericity ( 0 Dok.)
• 57M40 Characterizations of $E^3$ and $S^3$ (Poincare conjecture), See also {57N12} ( 0 Dok.)
• 57M50 Geometric structures on low-dimensional manifolds ( 0 Dok.)
• 57M60 Group actions in low dimensions ( 0 Dok.)
• 57M99 None of the above but in this section ( 0 Dok.)
• 57Nxx Topological manifolds ( 0 Dok. )
• 57N05 Topology of $E^2$, $2$-manifolds ( 0 Dok.)
• 57N10 Topology of general $3$-manifolds, See also {57Mxx} ( 0 Dok.)
• 57N12 Topology of $E^3$ and $S^3$, See also {57M40} ( 0 Dok.)
• 57N13 Topology of $E^4$, $4$-manifolds, See also {14Jxx, 32Jxx} ( 0 Dok.)
• 57N15 Topology of $E^n$, $n$-manifolds ($4 less n less infty$) ( 0 Dok.)
• 57N17 Topology of topological vector spaces ( 0 Dok.)
• 57N20 Topology of infinite-dimensional manifolds, See Also { 58Bxx} ( 0 Dok.)
• 57N25 Shapes, See also {54C56, 55P55, 55Q07} ( 0 Dok.)
• 57N30 Engulfing ( 0 Dok.)
• 57N35 Embeddings and immersions ( 0 Dok.)
• 57N37 Isotopy and pseudo-isotopy ( 0 Dok.)
• 57N40 Neighborhoods of submanifolds ( 0 Dok.)
• 57N45 Flatness and tameness ( 0 Dok.)
• 57N50 $S^{n-1}subset E^n$, Schoenflies problem ( 0 Dok.)
• 57N55 Microbundles and block bundles, See also {55R60, 57Q50} ( 0 Dok.)
• 57N60 Cellularity ( 0 Dok.)
• 57N65 Algebraic topology of manifolds ( 0 Dok.)
• 57N70 Cobordism and concordance ( 0 Dok.)
• 57N75 General position and transversality ( 0 Dok.)
• 57N80 Stratifications ( 0 Dok.)
• 57N99 None of the above but in this section ( 0 Dok.)
• 57Pxx Generalized manifolds, See also {18F15} ( 0 Dok. )
• 57P05 Local properties of generalized manifolds ( 0 Dok.)
• 57P10 Poincare duality spaces ( 0 Dok.)
• 57P99 None of the above but in this section ( 0 Dok.)
• 57Qxx PL-topology ( 0 Dok. )
• 57Q05 General topology of complexes ( 0 Dok.)
• 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc., See also {19B28} ( 0 Dok.)
• 57Q12 Wall finiteness obstruction for CW-complexes ( 0 Dok.)
• 57Q15 Triangulating manifolds ( 0 Dok.)
• 57Q20 Cobordism ( 0 Dok.)
• 57Q25 Comparison of PL-structures: classification, Hauptvermutung ( 0 Dok.)
• 57Q30 Engulfing ( 0 Dok.)
• 57Q35 Embeddings and immersions ( 0 Dok.)
• 57Q37 Isotopy ( 0 Dok.)
• 57Q40 Regular neighborhoods ( 0 Dok.)
• 57Q45 Knots and links (in high dimensions), {For the low-dimensional case, See 57M25} ( 0 Dok.)
• 57Q50 Microbundles and block bundles, See also {55R60, 57N55} ( 0 Dok.)
• 57Q55 Approximations ( 0 Dok.)
• 57Q60 Cobordism and concordance ( 0 Dok.)
• 57Q65 General position and transversality ( 0 Dok.)
• 57Q91 Equivariant PL-topology ( 0 Dok.)
• 57Q99 None of the above but in this section ( 0 Dok.)
• 57Rxx Differential topology, {For foundational questions of differentiable manifolds, See 58Axx; for infinite-dimensional manifolds, See 58Bxx} ( 0 Dok. )
• 57R05 Triangulating ( 0 Dok.)
• 57R10 Smoothing ( 0 Dok.)
• 57R12 Smooth approximations ( 0 Dok.)
• 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) ( 0 Dok.)
• 57R19 Algebraic topology on manifolds ( 0 Dok.)
• 57R20 Characteristic classes and numbers ( 0 Dok.)
• 57R22 Topology of vector bundles and fiber bundles, See Also {55Rxx} ( 0 Dok.)
• 57R25 Vector fields, frame fields ( 0 Dok.)
• 57R27 Controllability of vector fields on $C^infty$ and real-analytic manifolds, See also {49Qxx, 58F40, 93B05} ( 0 Dok.)
• 57R30 Foliations; geometric theory ( 0 Dok.)
• 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology, See also {58H10} ( 0 Dok.)
• 57R35 Differentiable mappings ( 0 Dok.)
• 57R40 Embeddings ( 0 Dok.)
• 57R42 Immersions ( 0 Dok.)
• 57R45 Singularities of differentiable mappings ( 0 Dok.)
• 57R50 Diffeomorphisms ( 0 Dok.)
• 57R52 Isotopy ( 0 Dok.)
• 57R55 Differentiable structures ( 0 Dok.)
• 57R57 Applications of global analysis to structures on manifolds, See also {58-XX} ( 0 Dok.)
• 57R60 Homotopy spheres, Poincare conjecture ( 0 Dok.)
• 57R65 Surgery and handlebodies ( 0 Dok.)
• 57R67 Surgery obstructions, Wall groups, See also {19J25} ( 0 Dok.)
• 57R70 Critical points and critical submanifolds ( 0 Dok.)
• 57R75 O- and SO-cobordism ( 0 Dok.)
• 57R77 Complex cobordism (U- and SU-cobordism), See also {55N22} ( 0 Dok.)
• 57R80 $h$- and $s$-cobordism ( 0 Dok.)
• 57R85 Equivariant cobordism ( 0 Dok.)
• 57R90 Other types of cobordism See{55N22} ( 0 Dok.)
• 57R91 Equivariant algebraic topology of manifolds ( 0 Dok.)
• 57R95 Realizing cycles by submanifolds ( 0 Dok.)
• 57R99 None of the above but in this section ( 0 Dok.)
• 57Sxx Topological transformation groups, See also {20F34, 22-XX, 54H15, 58D05} ( 0 Dok. )
• 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms ( 0 Dok.)
• 57S10 Compact groups of homeomorphisms ( 0 Dok.)
• 57S15 Compact Lie groups of differentiable transformations ( 0 Dok.)
• 57S17 Finite transformation groups ( 0 Dok.)
• 57S20 Noncompact Lie groups of transformations ( 0 Dok.)
• 57S25 Groups acting on specific manifolds ( 0 Dok.)
• 57S30 Discontinuous groups of transformations ( 0 Dok.)
• 57S99 None of the above but in this section ( 0 Dok.)
• 57Txx Homology and homotopy of topological groups and related structures ( 0 Dok. )
• 57T05 Hopf algebras, See also {16W30} ( 0 Dok.)
• 57T10 Homology and cohomology of Lie groups ( 0 Dok.)
• 57T15 Homology and cohomology of homogeneous spaces of Lie groups ( 0 Dok.)
• 57T20 Homotopy groups of topological groups and homogeneous spaces ( 0 Dok.)
• 57T25 Homology and cohomology of ${H}$-spaces ( 0 Dok.)
• 57T30 Bar and cobar constructions, See also {18G55, 55Uxx} ( 0 Dok.)
• 57T35 Applications of Eilenberg-Moore spectral sequences, See also {55R20, 55T20} ( 0 Dok.)
• 57T99 None of the above but in this section ( 0 Dok.)