Category:Homotopy theory

In algebraic topology, homotopy theory is the study of homotopy groups; and more generally of the category of topological spaces and homotopy classes of continuous mappings. At an intuitive level, a homotopy class is a connected component of a function space. The actual definition uses paths of functions.

Subcategories

This category has the following 2 subcategories, out of 2 total.

F

• ► Fiber bundles‎ (3 C, 38 P)

S

• ► Surgery theory‎ (28 P)

Pages in category "Homotopy theory"

The following 107 pages are in this category, out of 107 total. This list may not reflect recent changes (learn more).

Highly structured ring spectrum Homotopy 2 2-group A A¹ homotopy theory Acyclic space Adams filtration Adams spectral sequence Frank Adams Andreotti–Frankel theorem André–Quillen cohomology Aspherical space B Barratt–Priddy theorem Bott periodicity theorem Brown's representability theorem C Chromatic spectral sequence Classifying space Classifying space for U(n) Cofibration Cohomotopy group Compactly generated space Contractible space Cotangent complex Covering space CW complex D Direct limit of groups Double groupoid E EHP spectral sequence Eilenberg–MacLane space Equivariant cohomology Exterior space F Fiber bundle Fibrant object Fibration Freudenthal suspension theorem Fundamental group G Generalized Poincaré conjecture

G cont. Groupoid H H-space Homotopy analysis method Homotopy category Homotopy extension property Homotopy fiber Homotopy group Homotopy groups of spheres Talk:Homotopy groups of spheres/table Homotopy lifting property Homotopy sphere Homotopy type theory Hopf fibration Hopf invariant Hurewicz theorem I Iterated monodromy group J J-homomorphism Johnson–Wilson theory K Kan fibration L Line bundle Localization of a topological space Loop space M May spectral sequence Model category Monodromy N N-connected N-group (category theory) Nilpotence theorem Novikov conjecture O Obstruction theory P Path (topology) Peripheral subgroup Phantom map Plus construction Pointed space Postnikov system

P cont. Puppe sequence Q Quillen adjunction R Rational homotopy theory Ravenel conjectures Ring spectrum (homotopy theory) S Section (fiber bundle) Segal conjecture Seifert–van Kampen theorem Semi-locally simply connected Semi-s-cobordism Shape theory (mathematics) Simple-homotopy equivalence Simplex category Simplicial set Smash product Spanier–Whitehead duality Spectrum (homotopy theory) Sphere spectrum Stable homotopy theory Stable module category Stunted projective space Sullivan conjecture Dennis Sullivan Suspension (topology) T Timelike homotopy Timelike simply connected Toda bracket Topological half-exact functor Topological rigidity U Universal bundle W Weak equivalence (homotopy theory) Weakly contractible Wedge sum Whitehead product Whitehead theorem