Classification Search Result

Mathematics Subject Classification – MSC2020

55-XX

Algebraic topology

33160

55Pxx

Homotopy theory {For simple homotopy type, see 57Q10}

10611

55P05

Homotopy extension properties, cofibrations in algebraic topology

315

55P10

Homotopy equivalences in algebraic topology

1233

55P15

Classification of homotopy type

1141

55P20

Eilenberg-Mac Lane spaces

346

55P25

Spanier-Whitehead duality

104

55P30

Eckmann-Hilton duality

55P35

Loop spaces

1178

55P40

Suspensions

304

55P42

Stable homotopy theory, spectra

1445

55P43

Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)

387

55P45

\(H\)-spaces and duals

747

55P47

Infinite loop spaces

347

55P48

Loop space machines and operads in algebraic topology [See also 18Mxx]

454

55P50

String topology

105

55P55

Shape theory [See also 54C56, 55Q07]

854

55P57

Proper homotopy theory

55P60

Localization and completion in homotopy theory

940

55P62

Rational homotopy theory

1276

55P65

Homotopy functors in algebraic topology

267

55P91

Equivariant homotopy theory in algebraic topology [See also 19L47]

712

55P92

Relations between equivariant and nonequivariant homotopy theory in algebraic topology

55P99

None of the above, but in this section

1210

Overview

General and overarching topics; collections

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory; homological algebra

\(K\)-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximations and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

Convex and discrete geometry

Differential geometry

General topology

Algebraic topology

Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

Statistics

Numerical analysis

Computer science

Mechanics of particles and systems

Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

Classical thermodynamics, heat transfer

Quantum theory

Statistical mechanics, structure of matter

Relativity and gravitational theory

Astronomy and astrophysics

Geophysics

Operations research, mathematical programming

Game theory, economics, finance, and other social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication theory, circuits

Mathematics education

any	anywhere
cc	classification code
ct	classification text

a & b	logical and
abc*	right wildcard
a \| b	logical or
"ab c"	phrase
!ab	logical not
(ab c)	parentheses

Examples

Fields

Operators

Mathematics Subject Classification – MSC2020

Overview