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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] 26227

18Fxx

Categories and geometry 3655

18F99

None of the above, but in this section 231

19-XX

$K$-theory [See also 16E20, 18F25] 6755

19Exx

$K$-theory in geometry 858

19E99

None of the above, but in this section 37

20-XX

Group theory and generalizations 105717

20Fxx

Special aspects of infinite or finite groups 24249

20F70

Algebraic geometry over groups; equations over groups 191

32-XX

Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12] 43684

32Bxx

Local analytic geometry [See also 13-XX and 14-XX] 1774

32B99

None of the above, but in this section 135

32Jxx

Compact analytic spaces [For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx] 2558

32J25

Transcendental methods of algebraic geometry [See also 14C30] 632

34-XX

Ordinary differential equations 170910

34Cxx

Qualitative theory [See also 37-XX] 49732

34C08

Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.) 315

37-XX

Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] 106706

37Jxx

Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx] 17025

37J05

General theory, relations with symplectic geometry and topology 1221

37Kxx

Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] 16827

37K20

Relations with algebraic geometry, complex analysis, special functions [See also 14H70] 769

37K25

Relations with differential geometry 612

46-XX

Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx] 119092

46Bxx

Normed linear spaces and Banach spaces; Banach lattices [For function spaces, see 46Exx] 22407

46B20

Geometry and structure of normed linear spaces 7476

46Cxx

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4744

46C05

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1752

46Lxx

Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 22679

46L87

Noncommutative differential geometry [See also 58B32, 58B34, 58J22] 1422

51-XX

Geometry [For algebraic geometry, see 14-XX] 34256

51-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 43

51-01

Instructional exposition (textbooks, tutorial papers, etc.) 1397

51-02

Research exposition (monographs, survey articles) 467

51-03

Historical (must also be assigned at least one classification number from Section 01) 1331

51-04

Explicit machine computation and programs (not the theory of computation or programming) 217

51-06

Proceedings, conferences, collections, etc. 272

51Axx

Linear incidence geometry 4804

51A05

General theory and projective geometries 718

51A10

Homomorphism, automorphism and dualities 319

51A20

Configuration theorems 510

51A25

Algebraization [See also 12Kxx, 20N05] 380

51A50

Polar geometry, symplectic spaces, orthogonal spaces 437

51A99

None of the above, but in this section 341

51Bxx

Nonlinear incidence geometry 1287

51B05

General theory 346

51B99

None of the above, but in this section 89

51Cxx

Ring geometry (Hjelmslev, Barbilian, etc.) 368

51C05

Ring geometry (Hjelmslev, Barbilian, etc.) 364

51C99

None of the above, but in this section 3

51Dxx

Geometric closure systems 679

51D25

Lattices of subspaces [See also 05B35] 154

51Exx

Finite geometry and special incidence structures 8443

51E05

General block designs [See also 05B05] 384

51E10

Steiner systems 579

51E23

Spreads and packing problems 271

51E24

Buildings and the geometry of diagrams 953

51E99

None of the above, but in this section 180

51Fxx

Metric geometry 2460

51F20

Congruence and orthogonality [See also 20H05] 224

51F25

Orthogonal and unitary groups [See also 20H05] 220

51F99

None of the above, but in this section 808

51Hxx

Topological geometry 744

51H05

General theory 38

51H99

None of the above, but in this section 48

51Kxx

Distance geometry 904

51K05

General theory 529

51K10

Synthetic differential geometry 226

51K99

None of the above, but in this section 189

51Lxx

Geometric order structures [See also 53C75] 119

51L05

Geometry of orders of nondifferentiable curves 12

51L20

Geometry of orders of surfaces 18

51Mxx

Real and complex geometry 11554

51M16

Inequalities and extremum problems [For convex problems, see 52A40] 820

51M25

Length, area and volume [See also 26B15] 1104

51M35

Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15] 310

51M99

None of the above, but in this section 685

51Nxx

Analytic and descriptive geometry 6678

51N05

Descriptive geometry [See also 65D17, 68U07] 1187

51N10

Affine analytic geometry 956

51N15

Projective analytic geometry 1250

51N20

Euclidean analytic geometry 1959

51N25

Analytic geometry with other transformation groups 489

51N30

Geometry of classical groups [See also 20Gxx, 14L35] 201

51N35

Questions of classical algebraic geometry [See also 14Nxx] 864

51N99

None of the above, but in this section 470

51Pxx

Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) 312

51P05

Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) 304

51P99

None of the above, but in this section 5

52-XX

Convex and discrete geometry 30742

52-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 10

52-01

Instructional exposition (textbooks, tutorial papers, etc.) 203

52-02

Research exposition (monographs, survey articles) 402

52-03

Historical (must also be assigned at least one classification number from Section 01) 110

52-04

Explicit machine computation and programs (not the theory of computation or programming) 195

52-06

Proceedings, conferences, collections, etc. 269

52Axx

General convexity 14888

52A05

Convex sets without dimension restrictions 774

52A07

Convex sets in topological vector spaces [See also 46A55] 780

52A21

Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx] 630

52A22

Random convex sets and integral geometry [See also 53C65, 60D05] 1241

52A35

Helly-type theorems and geometric transversal theory 697

52A38

Length, area, volume [See also 26B15, 28A75, 49Q20] 919

52A39

Mixed volumes and related topics 412

52A40

Inequalities and extremum problems 3451

52A41

Convex functions and convex programs [See also 26B25, 90C25] 748

52Bxx

Polytopes and polyhedra 9211

52B20

Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 987

52B22

Shellability 96

52B35

Gale and other diagrams 70

52B40

Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx] 450

52B55

Computational aspects related to convexity [For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx] [See also 68Uxx] 1149

52Cxx

Discrete geometry 9222

52C10

Erdős problems and related topics of discrete geometry [See also 11Hxx] 734

52C15

Packing and covering in $2$ dimensions [See also 05B40, 11H31] 844

52C17

Packing and covering in $n$ dimensions [See also 05B40, 11H31] 2254

52C20

Tilings in $2$ dimensions [See also 05B45, 51M20] 1049

52C22

Tilings in $n$ dimensions [See also 05B45, 51M20] 882