Finite part of operator \(K\)-theory for groups with rapid decay (Q893793)

The article is devoted to the \(K\)-theory of the reduced \(C^*\)-algebras. The latter is generated from the group elements of finite orders. To each such element an idempotent of the group algebra is counterposed. Particularly, groups with a rapid decay property (RD) are considered. For them a sufficient condition is elaborated on the growth of conjugacy classes for a group to have the RD property. Imposing such condition lower bounds for structure groups of certain manifolds are estimated. The \(K\)-theory generated by torsion elements is utilized for this purpose.