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  5. The second homology of SL_2 of S-integers
 
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The second homology of SL_2 of S-integers

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Download h2sl2_feb15.pdf227.19 KB
Author(s)
Hutchinson, Kevin 
Uri
http://hdl.handle.net/10197/8209
Date Issued
February 2016
Date Available
01T02:00:14Z February 2018
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
Journal
Journal of Number Theory
Volume
159
Start Page
223
End Page
272
Copyright (Published Version)
2015 Elsevier
Keywords
  • K-theory

  • Group homology

DOI
10.1016/j.jnt.2015.07.022
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
Owning collection
Mathematics and Statistics Research Collection
Scopus© citations
4
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Feb 3, 2023
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