Ring and module structures on $K$-theory of leaf spaces and their application to longitudinal index theory

Abstract

Pursuing conjectures of John Roe, we use the stable Higson corona of foliated cones to construct a new $K$-theory model for the leaf space of a foliation. This new $K$-theory model is -- in contrast to Alain Connes' $K$-theory model -- a ring. We show that Connes' $K$-theory model is a module over this ring and develop an interpretation of the module multiplication in terms of indices of twisted longitudinally elliptic operators.

Accepted for publication by the Journal of Topology

Cited by in corpus (2)

• Warped cones over profinite completions
• Secondary cup and cap products in coarse geometry