Homology stability for the special linear group of a field and Milnor-Witt K-theory
|Title:||Homology stability for the special linear group of a field and Milnor-Witt K-theory||Authors:||Hutchinson, Kevin
|Permanent link:||http://hdl.handle.net/10197/6586||Date:||Jun-2010||Abstract:||Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism Hn(SLt(F), Z) → Hn(SLt+1(F), Z). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n + 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. fn,n is an isomorphism when n is odd and when n is even the kernel is isomorphic to I n+1(F), the (n + 1)st power of the fundamental ideal of the Witt Ring of F. When n is even the cokernel of fn−1,n is isomorphic to KMW n (F), the nth Milnor-Witt K-theory group of F. When n is odd, the cokernel of fn−1,n is isomorphic to 2KM n (F), where KM n (F) is the nth Milnor K-group of F.||Type of material:||Journal Article||Publisher:||Universität Bielefeld||Journal:||Documenta Mathematica||Volume:||Extra volume: Andrea A. Suslin's Sixieth Birthday||Start page:||267||End page:||315||Keywords:||K-theory; Special linear group; Group homology||Other versions:||https://www.math.uni-bielefeld.de/documenta/vol-suslin/hutchinson_tao.html||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
Show full item record
Page view(s) 5022
This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.