Ring structures in coarse K-theory

  • The K-theory of the stable Higson corona of a coarse space carries a canonical ring structure. The present thesis covers two aspects of this ring: Chapter 1: The K-theory of the stable Higson corona is the domain of an unreduced version of the coarse co-assembly map of Emerson and Meyer. We show that the target also carries a ring structure and co-assembly is a ring homomorphism, provided that the given coarse space is contractible in a coarse sense. Chapter 2 (pursuing conjectures of John Roe): Applied to a foliated cone over a foliation, we show that the K-theory of the stable Higson corona can be considered as a new model for the K-theory of the leaf space, which is - in contrast to 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 structure in terms of twisted longitudinally elliptic operators.

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Author:Christopher Wulff
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/3165
Advisor:Bernhard Hanke
Type:Doctoral Thesis
Publishing Institution:Universität Augsburg
Granting Institution:Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät
Date of final exam:2015/06/25
Release Date:2015/08/26
Tag:coarse geometry; co-assembly; K-theory; foliation index theory; ring and module structures
GND-Keyword:K-Theorie; Indextheorie; Ringstruktur
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand