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

Subcategories

There are 6 subcategories to this category.

H

• Homological algebra
• Homology theory
• Homotopy theory

K

• K-theory
• Knot theory

T

• Topological graph theory

Articles in category "Algebraic topology"

There are 88 articles in this category.

3-sphere A Abstract polytope Adams operation Alexander-Spanier cohomology Algebraic topology Associated bundle B Barycentric subdivision Betti number Borsuk-Ulam theorem Bott periodicity theorem C CW complex Canonical line bundle Categorification Cech cohomology Chain (algebraic topology) Characteristic class Chern class Chern-Simons form Classifying space Cocycle class Cohomology Cohomology operation Combinatorial topology Cone (topology) Covering map Cup product D De Rham cohomology Degree (mathematics) E Eilenberg-MacLane space

E cont. Euler characteristic F Facet (mathematics) Fiber bundle Fibration Formal group law Free product Fundamental class Fundamental group G Genus (mathematics) H H-space Hairy ball theorem Homological algebra Homology theory Homotopical algebra Homotopy Homotopy lifting property Hopf bundle Hurewicz theorem I Intersection cohomology Invariance of domain K K-theory Knot theory Künneth theorem L Line bundle List of algebraic topology topics List of homological algebra topics Lyusternik-Schnirelmann category M Mapping cone Mapping cylinder Monodromy

M cont. Morava K-theory P Plus construction Polychoron Polytope Pontryagin class Pontryagin number R Ramification Real projective space Riemann-Hurwitz formula S Seifert-van Kampen theorem Sheaf Sheaf cohomology Simplicial approximation theorem Simplicial complex Simplicial set Simply connected space Spectral sequence Spinor bundle Stiefel-Whitney class Swan's theorem T Tesseract Thom space Todd class Triangulation (topology) U Universal coefficient theorem V Vector bundle W Weil conjectures Whitehead torsion Winding number