In mathematics, particularly algebraic topology, the Kan-Thurston theorem associates a discrete group
to every path-connected topological space
might then be regarded as a good approximation to the space
, and consequently the theorem is sometimes interpreted to mean that homotopy theory can be viewed as part of group theory.
More precisely,[1] the theorem states that every path-connected topological space is homology-equivalent to the classifying space
, where homology-equivalent means there is a map
The theorem is attributed to Daniel Kan and William Thurston who published their result in 1976.
be a path-connected topological space.