 

Claude L. Schochet
A Pext primer: Pure extensions and lim^{1} for infinite abelian groups


Published: 
June 29, 2003 
Keywords: 
Pure extensions, Pext^{1}_{Z}(G,H), lim^{1}, Jensen's Theorem, infinite abelian groups, quasidiagonality, phantom maps 
Subject: 
Primary: 20K35, 19K35, 46L80. Secondary: 18E25, 18G15, 20K40, 20K45, 47L80, 55U99 


Abstract
The abelian group $\Pext GH$ of pure extensions has recently attracted the interest of workers in noncommutative topology, especially those using $KK$theory, since under minimal hypotheses the closure of zero in the Kasparov group $KK_*(A,B)$ (for separable $C^*$algebras $A$ and $B$) is isomorphic to the group \[ \Pext{K_*(A)}{K_*(B)}. \] As $K_*(A)$ and $K_*(B)$ can take values in all countable abelian groups, assuming that $G$ and $H$ are countable is natural.
In this mostly expository work we survey the known (and not so wellknown) properties of $\pext$ and its relationship to $\lim ^1 $ and develop some new results on their computation.


Author information
Department of Mathematics, Wayne State University, Detroit, MI 48202
claude@math.wayne.edu 
