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The second homology of SL_2 of S-integers
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| File | Description | Size | Format | |
|---|---|---|---|---|
| h2sl2_feb15.pdf | 227.19 kB | Adobe PDF | Download |
| 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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