Ring and module structures on $K$-theory of leaf spaces and their application to longitudinal index theory
| Autor: | Christopher Wulff |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Ring (mathematics) Mathematics::Operator Algebras Index (typography) 010102 general mathematics Primary 19K56 Secondary 46L80 46L87 57R30 58J22 K-Theory and Homology (math.KT) Space (mathematics) K-theory 01 natural sciences Interpretation (model theory) 010101 applied mathematics Multiplication (music) Elliptic operator Mathematics::K-Theory and Homology Mathematics - K-Theory and Homology Foliation (geology) FOS: Mathematics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Journal of Topology |
| DOI: | 10.48550/arxiv.1510.04470 |
| Popis: | 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. Comment: Accepted for publication by the Journal of Topology |
| Databáze: | OpenAIRE |
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