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Mathematics Subject Classification – MSC2020
55-XX
Algebraic topology
32302
55Pxx
Homotopy theory
{For simple homotopy type, see
57Q10
}
10370
55P05
Homotopy extension properties, cofibrations in algebraic topology
312
55P10
Homotopy equivalences in algebraic topology
1210
55P15
Classification of homotopy type
1098
55P20
Eilenberg-Mac Lane spaces
336
55P25
Spanier-Whitehead duality
102
55P30
Eckmann-Hilton duality
83
55P35
Loop spaces
1152
55P40
Suspensions
299
55P42
Stable homotopy theory, spectra
1397
55P43
Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)
368
55P45
\(H\)-spaces and duals
743
55P47
Infinite loop spaces
339
55P48
Loop space machines and operads in algebraic topology
[See also
18Mxx
]
427
55P50
String topology
102
55P55
Shape theory
[See also
54C56
,
55Q07
]
848
55P57
Proper homotopy theory
37
55P60
Localization and completion in homotopy theory
918
55P62
Rational homotopy theory
1238
55P65
Homotopy functors in algebraic topology
260
55P91
Equivariant homotopy theory in algebraic topology
[See also
19L47
]
678
55P92
Relations between equivariant and nonequivariant homotopy theory in algebraic topology
26
55P99
None of the above, but in this section
1191
Overview
00
General and overarching topics; collections
01
History and biography
03
Mathematical logic and foundations
05
Combinatorics
06
Order, lattices, ordered algebraic structures
08
General algebraic systems
11
Number theory
12
Field theory and polynomials
13
Commutative algebra
14
Algebraic geometry
15
Linear and multilinear algebra; matrix theory
16
Associative rings and algebras
17
Nonassociative rings and algebras
18
Category theory; homological algebra
19
\(K\)-theory
20
Group theory and generalizations
22
Topological groups, Lie groups
26
Real functions
28
Measure and integration
30
Functions of a complex variable
31
Potential theory
32
Several complex variables and analytic spaces
33
Special functions
34
Ordinary differential equations
35
Partial differential equations
37
Dynamical systems and ergodic theory
39
Difference and functional equations
40
Sequences, series, summability
41
Approximations and expansions
42
Harmonic analysis on Euclidean spaces
43
Abstract harmonic analysis
44
Integral transforms, operational calculus
45
Integral equations
46
Functional analysis
47
Operator theory
49
Calculus of variations and optimal control; optimization
51
Geometry
52
Convex and discrete geometry
53
Differential geometry
54
General topology
55
Algebraic topology
57
Manifolds and cell complexes
58
Global analysis, analysis on manifolds
60
Probability theory and stochastic processes
62
Statistics
65
Numerical analysis
68
Computer science
70
Mechanics of particles and systems
74
Mechanics of deformable solids
76
Fluid mechanics
78
Optics, electromagnetic theory
80
Classical thermodynamics, heat transfer
81
Quantum theory
82
Statistical mechanics, structure of matter
83
Relativity and gravitational theory
85
Astronomy and astrophysics
86
Geophysics
90
Operations research, mathematical programming
91
Game theory, economics, finance, and other social and behavioral sciences
92
Biology and other natural sciences
93
Systems theory; control
94
Information and communication theory, circuits
97
Mathematics education
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