L-theory of C*-algebras

Landthaler, Markus; Nikolaus, Thomas und Schlichting, Marco (2023): L-theory of C*-algebras. In: Proceedings of the London Mathematical Society, Bd. 127, Nr. 5: S. 1451-1506

Abstract

We establish a formula for the L-theory spectrum of real C*-algebras from which we deduce a presentation of the L-groups in terms of the topological K-groups, extending all previously known results of this kind. Along the way, we extend the integral comparison map obtained in previous work by the first two authors to real C*-algebras and interpret it using topological Grothendieck–Witt theory. Finally, we use our results to give an integral comparison between the Baum–Connes conjecture and the L-theoretic Farrell–Jones conjecture, and discuss our comparison map in terms of the signature operator on oriented manifolds.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0024-6115
• Sprache: Englisch