Bounds for the rank of the finite part of operator K-theory


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Samurkas S. K.

JOURNAL OF NONCOMMUTATIVE GEOMETRY, vol.14, no.2, pp.413-439, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.4171/jncg/333
  • Journal Name: JOURNAL OF NONCOMMUTATIVE GEOMETRY
  • Journal Indexes: Science Citation Index Expanded, Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.413-439
  • Keywords: Finite part of operator K-theory, structure group, positive scalar curvature metric, polynomially full groups, NOVIKOV-CONJECTURE

Abstract

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 oriented manifold M.