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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] 26385

18Fxx

Categories and geometry 3668

18F99

None of the above, but in this section 233

19-XX

$K$-theory [See also 16E20, 18F25] 6801

19Exx

$K$-theory in geometry 865

19E99

None of the above, but in this section 37

20-XX

Group theory and generalizations 106209

20Fxx

Special aspects of infinite or finite groups 24379

20F70

Algebraic geometry over groups; equations over groups 192

32-XX

Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12] 43883

32Bxx

Local analytic geometry [See also 13-XX and 14-XX] 1777

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] 2564

32J25

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

34-XX

Ordinary differential equations 172214

34Cxx

Qualitative theory [See also 37-XX] 50041

34C08

Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.) 318

37-XX

Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] 107644

37Jxx

Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx] 17084

37J05

General theory, relations with symplectic geometry and topology 1233

37Kxx

Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] 16926

37K20

Relations with algebraic geometry, complex analysis, special functions [See also 14H70] 776

37K25

Relations with differential geometry 617

46-XX

Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx] 119562

46Bxx

Normed linear spaces and Banach spaces; Banach lattices [For function spaces, see 46Exx] 22497

46B20

Geometry and structure of normed linear spaces 7498

46Cxx

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4754

46C05

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1758

46Lxx

Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 22810

46L87

Noncommutative differential geometry [See also 58B32, 58B34, 58J22] 1430

51-XX

Geometry [For algebraic geometry, see 14-XX] 34375

51-00

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

51-01

Instructional exposition (textbooks, tutorial papers, etc.) 1404

51-02

Research exposition (monographs, survey articles) 467

51-03

Historical (must also be assigned at least one classification number from Section 01) 1336

51-04

Explicit machine computation and programs (not the theory of computation or programming) 218

51-06

Proceedings, conferences, collections, etc. 273

51Axx

Linear incidence geometry 4813

51A05

General theory and projective geometries 722

51A10

Homomorphism, automorphism and dualities 321

51A20

Configuration theorems 511

51A25

Algebraization [See also 12Kxx, 20N05] 380

51A50

Polar geometry, symplectic spaces, orthogonal spaces 440

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 680

51D25

Lattices of subspaces [See also 05B35] 154

51Exx

Finite geometry and special incidence structures 8465

51E05

General block designs [See also 05B05] 385

51E10

Steiner systems 581

51E23

Spreads and packing problems 271

51E24

Buildings and the geometry of diagrams 957

51E99

None of the above, but in this section 181

51Fxx

Metric geometry 2471

51F20

Congruence and orthogonality [See also 20H05] 226

51F25

Orthogonal and unitary groups [See also 20H05] 220

51F99

None of the above, but in this section 814

51Hxx

Topological geometry 743

51H05

General theory 38

51H99

None of the above, but in this section 48

51Kxx

Distance geometry 909

51K05

General theory 531

51K10

Synthetic differential geometry 228

51K99

None of the above, but in this section 191

51Lxx

Geometric order structures [See also 53C75] 120

51L05

Geometry of orders of nondifferentiable curves 12

51L20

Geometry of orders of surfaces 19

51Mxx

Real and complex geometry 11610

51M16

Inequalities and extremum problems [For convex problems, see 52A40] 828

51M25

Length, area and volume [See also 26B15] 1113

51M35

Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15] 311

51M99

None of the above, but in this section 685

51Nxx

Analytic and descriptive geometry 6696

51N05

Descriptive geometry [See also 65D17, 68U07] 1188

51N10

Affine analytic geometry 956

51N15

Projective analytic geometry 1251

51N20

Euclidean analytic geometry 1968

51N25

Analytic geometry with other transformation groups 493

51N30

Geometry of classical groups [See also 20Gxx, 14L35] 202

51N35

Questions of classical algebraic geometry [See also 14Nxx] 865

51N99

None of the above, but in this section 472

51Pxx

Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) 318

51P05

Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) 309

51P99

None of the above, but in this section 6

52-XX

Convex and discrete geometry 30907

52-00

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

52-01

Instructional exposition (textbooks, tutorial papers, etc.) 206

52-02

Research exposition (monographs, survey articles) 403

52-03

Historical (must also be assigned at least one classification number from Section 01) 112

52-04

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

52-06

Proceedings, conferences, collections, etc. 271

52Axx

General convexity 14947

52A05

Convex sets without dimension restrictions 775

52A07

Convex sets in topological vector spaces [See also 46A55] 783

52A21

Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx] 634

52A22

Random convex sets and integral geometry [See also 53C65, 60D05] 1242

52A35

Helly-type theorems and geometric transversal theory 702

52A38

Length, area, volume [See also 26B15, 28A75, 49Q20] 924

52A39

Mixed volumes and related topics 412

52A40

Inequalities and extremum problems 3462

52A41

Convex functions and convex programs [See also 26B25, 90C25] 763

52Bxx

Polytopes and polyhedra 9287

52B20

Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 1004

52B22

Shellability 95

52B35

Gale and other diagrams 71

52B40

Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx] 465

52B55

Computational aspects related to convexity [For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx] [See also 68Uxx] 1156

52Cxx

Discrete geometry 9265

52C10

Erdős problems and related topics of discrete geometry [See also 11Hxx] 741

52C15

Packing and covering in $2$ dimensions [See also 05B40, 11H31] 851

52C17

Packing and covering in $n$ dimensions [See also 05B40, 11H31] 2258

52C20

Tilings in $2$ dimensions [See also 05B45, 51M20] 1053

52C22

Tilings in $n$ dimensions [See also 05B45, 51M20] 884