The third homology of the special linear group of a field

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Title: The third homology of the special linear group of a field
Authors: Hutchinson, Kevin
Tao, Liqun
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Date: Sep-2009
Abstract: We prove that for any infinite field F, the map H-3(SLn(F), Z) -> H-3(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(M) (F), where K-n(M)(F) is the nth Milnor K-group of F. We deduce that the natural homomorphism from H-3(SL2(F), Z) to the indecomposable K-3 of F, K-3(F)(ind), is surjective for any infinite field F.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Elsevier
Copyright (published version): 2009 Elsevier
Keywords: Milnor K-theoryQuadratic-formsTheoremSuslin
DOI: 10.1016/j.jpaa.2009.01.002
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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