Category:Algebraic topology

Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces.

The main article for this category is Algebraic topology.

Subcategories

This category has the following 15 subcategories, out of 15 total.

► Theorems in algebraic topology‎ (24 P) C ► Characteristic classes‎ (10 P) ► Cohomology theories‎ (32 P) D ► Digital topology‎ (4 P) F ► Fiber bundles‎ (3 C, 38 P)

H ► Homological algebra‎ (6 C, 102 P) ► Homology theory‎ (1 C, 47 P) ► Homotopy theory‎ (2 C, 107 P) I ► Intersection theory‎ (9 P) K ► K-theory‎ (1 C, 32 P)

K cont. ► Knot theory‎ (4 C, 71 P, 1 F) S ► Surgery theory‎ (28 P) T ► Topological graph theory‎ (1 C, 30 P) ► Topological methods of algebraic geometry‎ (1 C, 30 P) ► Topology of Lie groups‎ (1 C, 7 P)

Pages in category "Algebraic topology"

The following 194 pages are in this category, out of 194 total. This list may not reflect recent changes (learn more).

Algebraic topology Glossary of topology House with two rooms List of algebraic topology topics 3 3-sphere A A∞-operad Abstract polytope Abstract simplicial complex Acyclic space Adams operation Alexander duality Alexander–Spanier cohomology Algebraic cobordism Highly structured ring spectrum Quasitoric manifold Topological modular forms Algebraic topology (object) Aspherical space Associated bundle B Barycentric subdivision Betti number Bloch group Bockstein homomorphism Borsuk–Ulam theorem Brown–Peterson cohomology C Calculus of functors Cap product Cartan model Categorification Čech cohomology Chain (algebraic topology) Characteristic class Chern–Simons form Chern–Weil theory Classifying space Classifying space for O(n) Clique complex Cobordism Cocycle class Cohomology Cohomology operation Collapse (topology) Combinatorial map Combinatorial topology Complex cobordism Cone (topology) Covering space Crossed module Cup product CW complex D Degree of a continuous mapping Delta set Direct limit of groups Directed algebraic topology Dold manifold Doomsday conjecture Double torus knot Dunce hat (topology) Duocylinder Duoprism E E∞-operad Eilenberg–MacLane space Eilenberg–Ganea theorem Elliptic cohomology Equivariant cohomology

E cont. Esquisse d'un Programme Essential manifold Euler calculus Euler characteristic F Facet (disambiguation) Fiber bundle Fibration Formal group Free product Fundamental class Fundamental group G Ganea conjecture Generalized map Genus (mathematics) Godement resolution Good cover (algebraic topology) Gray's conjecture Gysin sequence H H-space Hattori–Stong theorem Higher-dimensional algebra Homeotopy Homology manifold Homology theory Homotopical algebra Homotopy extension property Homotopy fiber Homotopy lifting property Hopf fibration I Induced homomorphism (algebraic topology) Induced homomorphism (fundamental group) Infinite symmetric product Intersection homology Invariance of domain Inverse bundle Irreducible ideal J James embedding James reduced product Join (topology) L L-theory Lazard's universal ring Lehrbuch der Topologie Lie algebra bundle Line bundle List of cohomology theories List of homological algebra topics Local system Lusternik–Schnirelmann category M Mapping cone (topology) Mapping cylinder Massey product Mathai–Quillen formalism Metaplectic structure Microbundle Monodromy Moore space (algebraic topology) Morava K-theory N N-skeleton Nonholonomic system P Pair of spaces Peripheral subgroup Peterson–Stein formula Plus construction Poincaré complex Poincaré space

P cont. Polychoron Pontryagin cohomology operation Postnikov square Presentation complex Products in algebraic topology Projective bundle Pseudocircle Q Quasi-isomorphism R R-algebroid Ramification Real projective space Regular homotopy Riemann–Hurwitz formula Ring spectrum (homotopy theory) Rose (topology) S Secondary cohomology operation Section (fiber bundle) Semi-locally simply connected Semi-s-cobordism Serre spectral sequence Serre–Swan theorem Sheaf (mathematics) Sheaf cohomology Shelling (topology) Shriek map Simplex category Simplicial complex Simplicial homology Simplicial map Simplicial set Simply connected at infinity Simply connected space Size function Size functor Size homotopy group Size theory Solenoid (mathematics) Spectral sequence Sphere spectrum Spin structure Spinor bundle Spinor field Steenrod algebra String topology Surgery structure set Symplectic frame bundle Symplectic spinor bundle T Tesseract Thom space Timelike homotopy Timelike simply connected Topological combinatorics Topological degree theory Topological K-theory Topological pair Torus knot Triangulation (topology) Twisted Poincaré duality V Vanishing cycle Vector bundle Vietoris–Rips complex Virtual knot W Whitehead link Winding number