Finite Part of Operator $K$-Theory for Groups with Rapid Decay

@article{Gong2013FinitePO,
title={Finite Part of Operator \$K\$-Theory for Groups with Rapid Decay},
author={Sherry Gong},
journal={Journal of Noncommutative Geometry},
year={2013},
volume={9},
pages={697-706}
}

In this paper we study the part of the $K$-theory of the reduced $C^*$-algebra arising from torsion elements of the group, and in particular we study the pairing of $K$-theory with traces and when traces can detect certain $K$-theory elements. In the case of groups with Property RD, we give a condition on the growth of conjugacy classes that determines whether they can be detected. Moreover, in the case that they can be detected, we show that nonzero elements in the part of the $K$-theory… CONTINUE READING