La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

Question : CC = Bundle
14-XX Algebraic geometry

• 14D20 Algebraic moduli problems, moduli of vector bundles [For analytic moduli problems, see 32G13]
• 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 14D20
• 14F05 Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
• 14H60 Vector bundles on curves and their moduli [See also 14D20, 14F05]
• 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]

18-XX Category theory; homological algebra [For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology]

• 18F15 Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]

32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]

• 32G08 Deformations of fiber bundles
• 32L05 Holomorphic bundles and generalizations
• 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
• 32L15 Bundle convexity [See also 32F10]

46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]

• 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]

53-XX Differential geometry [For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx]

• 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
• 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]

55-XX Algebraic topology

• 55Rxx Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]
• 55R10 Fiber bundles
• 55R25 Sphere bundles and vector bundles
• 55R50 Stable classes of vector space bundles, K-theory [See also 19Lxx] [For algebraic K-theory, see 18F25, 19-XX]
• 55R60 Microbundles and block bundles [See also 57N55, 57Q50]
• 55R65 Generalizations of fiber spaces and bundles
• 55R91 Equivariant fiber spaces and bundles [See also 19L47]
• 55S40 Sectioning fiber spaces and bundles

57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]

• 57N55 Microbundles and block bundles [See also 55R60, 57Q50]
• 57Q50 Microbundles and block bundles [See also 55R60, 57N55]
• 57R22 Topology of vector bundles and fiber bundles [See also 55Rxx]

58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]

• 58A30 Vector distributions (subbundles of the tangent bundles)
• 58A32 Natural bundles [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 58A05, 58A20
• 58J52 Determinants and determinant bundles, analytic torsion [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 58G26

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