The second homology of SL_2 of S-integers
|Title:||The second homology of SL_2 of S-integers||Authors:||Hutchinson, Kevin||Permanent link:||http://hdl.handle.net/10197/8209||Date:||Feb-2016||Abstract:||We calculate the structure of the finitely generated groups H2(SL2(Z[1/m]),Z) when m is a multiple of 6. Furthermore, we show how to construct homology classes, represented by cycles in the bar resolution, which generate these groups and have prescribed orders. When n≥2 and m is the product of the first n primes, we combine our results with those of Jun Morita to show that the projection St(2,Z[1/m])→SL2(Z[1/m]) is the universal central extension. Our methods have wider applicability: The main result on the structure of the second homology of certain rings is valid for rings of S-integers with sufficiently many units. For a wide class of rings A , we construct explicit homology classes in H2(SL2(A),Z), functorially dependent on a pair of units, which correspond to symbols in K2(2,A).||Type of material:||Journal Article||Publisher:||Elsevier||Copyright (published version):||2015 Elsevier||Keywords:||K-theory; Group homology||DOI:||10.1016/j.jnt.2015.07.022||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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