On the third homology of SL_2 and weak homotopy invariance

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Title: On the third homology of SL_2 and weak homotopy invariance
Authors: Hutchinson, Kevin
Wendt, Matthias
Permanent link: http://hdl.handle.net/10197/8210
Date: 12-Nov-2015
Abstract: The goal of the paper is to achieve - in the special case of the linear group SL2 - some understanding of the relation between group homology and its A1-invariant replacement. We discuss some of the general properties of the A1-invariant group homology, such as stabilization sequences and Grothendieck-Witt module structures. Together with very precise knowledge about refined Bloch groups, these methods allow us to deduce that in general there is a rather large difference between group homology and its A1 -invariant version. In other words, weak homotopy invariance fails for SL2 over many families of non-algebraically closed fields.
Type of material: Journal Article
Publisher: American Mathematical Society
Journal: Transactions of the American Mathematical Society
Volume: 367
Issue: 10
Start page: 7481
End page: 7513
Copyright (published version): 2014 American Mathematical Society
Keywords: Weak homotopy invarianceGroup homology
Other versions: http://www.ams.org/journals/tran/2015-367-10/S0002-9947-2014-06495-7/
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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