Trace class operators, regulators, and assembly maps in -theory
Guillermo Cortiñas
Gisela Tartaglia
![Trace class operators, regulators, and assembly maps in $K$-theory cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-19.png&w=3840&q=90)
Abstract
Let be a group and let be homotopy algebraic -theory. We prove that if satisfies the rational isomorphism conjecture for the group algebra with coefficients in the algebra of trace-class operators in Hilbert space, then it also satisfies the -theoretic Novikov conjecture for the group algebra over the integers, and the rational injectivity part of the Farrell-Jones conjecture with coefficients in any number field.
Cite this article
Guillermo Cortiñas, Gisela Tartaglia, Trace class operators, regulators, and assembly maps in -theory. Doc. Math. 19 (2014), pp. 439–455
DOI 10.4171/DM/452