Algebraic K-Theory In Low Degree and The Novikov Assembly Map |
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| Authors: | Matthey, Michel Oyono-Oyono, Herve |
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| Affiliation: | SFB 478, Geometrische Strukturen in der Mathematik, Hittorfstrasse 27, D-48149 Münster, Germany; e-mail: mattheym{at}uni-muenster.de
Université Blaise Pascal, Clermont-Ferrand, Département de Mathématiques Complexe Scientifique des Cézeaux, F-63177 Aubière Cedex, France; e-mail: oyono{at}cedre.univ-bpclermont.fr |
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| Abstract: | We prove that the Novikov assembly map for a group  factorizes,in low homological degree, through the algebraicK-theory of its integral group ring. In homological degree 2,this answers a question posed by N. Higson and P. Julg. As adirect application, we prove that if is torsion-free and satisfiesthe Baum-Connes conjecture, then the homology group H1(; Z)injects in  and in  , for any ring A such that  . If moreover B is of dimension lessthan or equal to 4, then we show that H2(; Z) injects in  and in  , where A is as before, and  2 is generated by the Steinberg symbols{ ,}, for  . 2000 Mathematical Subject Classification: primary 19D55, 19Kxx,58J22; secondary: 19Cxx, 19D45, 43A20, 46L85. |
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| Keywords: | Novikov assembly map algebraic K-theory group rings group homology |
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