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
|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 invariance; Group 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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