The third homology of the special linear group of a field
|Title:||The third homology of the special linear group of a field||Authors:||Hutchinson, Kevin
|Permanent link:||http://hdl.handle.net/10197/6516||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-theory;Quadratic-forms;Theorem;Suslin||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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