Category
page 1Theorems in algebraic topology
hairy ball theorem
theorem which states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres
Borsuk–Ulam theorem
theorem
Seifert–van Kampen theorem
a theorem in topology describing the fundamental group of a space in terms of a cover of the space by two open path-connected subspaces
Poincaré duality
duality that relates homology and cohomology groups for oriented closed manifolds
Hurewicz theorem
theorem that relates homotopy groups to homology groups
Lefschetz fixed-point theorem
theorem
Künneth theorem
theorem
universal coefficient theorem
Establish relationships between homology and cohomology theories
Lefschetz hyperplane theorem
theorem that the inclusion between a projective variety and its hyperplane section induces isomorphisms of homology, cohomology or homotopy groups in low degrees
Milnor conjecture
simplicial approximation theorem
in algebraic topology, a theorem that a continuous map between (geometric realizations of) simplicial complexes is homotopy-equivalent to a simplicial map between subdivisions of the simplicial complexes
Eilenberg–Zilber theorem
theorem