The Hurewicz Theorem relates a topological space's homotopy groups to its homology groups, showing that for a simply connected space, the first nonvanishing homotopy group and the first nonvanishing homology group occur in the same dimension and are isomorphic there, with a corresponding map linking the two families of groups in every dimension. Named for Witold Hurewicz, it is a foundational bridge between algebraic topology's two principal families of invariants, homotopy and homology.
Facts
StatementA basic result of algebraic topology connecting homotopy theory with homology theory via the Hurewicz homomorphism. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Hurewicz theorem, Wikipedia
Principal Result Of
Source Witold Hurewicz (Wikipedia)
Proved By
Source Hurewicz theorem, Wikipedia
Sources
1. Hurewicz theorem, Wikipedia
Lead, first sentence
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism.
Proved By: Witold Hurewicz, Lead sentence
The theorem is named after Witold Hurewicz, and generalizes earlier results of Henri Poincaré.
In Branch: Algebraic Topology, Lead sentence
matics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map kn
In Group: Algebraic Topology, Lead paragraph
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism.
View the SourceWitold Hurewicz (Wikipedia)
Principal Result Of: Witold Hurewicz, CareerQuote, Principal Result Of: Witold Hurewicz, Career
the Hurewicz theorem connecting homotopy and homology groups
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