The second homology of SL_2 of S-integers

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Title: The second homology of SL_2 of S-integers
Authors: Hutchinson, Kevin
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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-theoryGroup 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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