Bounds for the rank of the finite part of operator $K$-Theory

@article{Samurka2017BoundsFT,
  title={Bounds for the rank of the finite part of operator \$K\$-Theory},
  author={S{\"u}leyman Kağan Samurkaş},
  journal={arXiv: K-Theory and Homology},
  year={2017}
}
  • Süleyman Kağan Samurkaş
  • Published 2017
  • Mathematics
  • arXiv: K-Theory and Homology
  • We derive a lower and an upper bound for the rank of the finite part of operator $K$-theory groups of maximal and reduced $C^*$-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy classes of finite order elements in the group. The upper bound is based on the amount of torsion elements in the group. We use the lower bound to give lower bounds for the structure group $S(M)$ and the group of positive scalar curvature metrics $P(M)$ for an… CONTINUE READING
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