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3 March 2014

  • 20:1420:14, 3 March 2014 diff hist +45 Hurewicz theorem The property "path-connected" is essential for the Hurewicz homomorphism to be the abelianization (cf. Hatcher: Algebraic Topology, §2.A, page 167). Regard (as a counterexample) a disjoint union of two 1-SPHERES. Then \pi_1=\Z and H_1=\Z\oplus\Z.
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