The Third Homology of the Special Linear Group of a Field
نویسندگان
چکیده
We prove that for any infinite field F , the map H3(SLn(F ), Z)→ H3(SLn+1(F ), Z) is an isomorphism for all n ≥ 3. When n = 2 the cokernel of this map is naturally isomorphic to 2 · K 3 (F ), where K n (F ) is the nth Milnor K-group of F . We deduce that the natural homomorphism from H3(SL2(F ), Z) to the indecomposable K3 of F , K3(F ), is surjective for any infinite field F .
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