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In mathematics, particularly algebraic top … In mathematics, particularly algebraic topology, the Kan-Thurston theorem associates a discrete group to every path-connected topological space in such a way that the group cohomology of is the same as the cohomology of the space . The group 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, the theorem states that every path-connected topological space is homology-equivalent to the classifying space of a discrete group , where homology-equivalent means there is a map inducing an isomorphism on homology. The theorem is attributed to Daniel Kan and William Thurston who published their result in 1976.urston who published their result in 1976.
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| rdfs:comment |
In mathematics, particularly algebraic top … In mathematics, particularly algebraic topology, the Kan-Thurston theorem associates a discrete group to every path-connected topological space in such a way that the group cohomology of is the same as the cohomology of the space . The group 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. The theorem is attributed to Daniel Kan and William Thurston who published their result in 1976.urston who published their result in 1976.
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Kan-Thurston theorem
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