TRACE CLASS OPERATORS, REGULATORS, AND ASSEMBLY MAPS IN K-THEORY

GUILLERMO CORTIÑAS; GISELA TARTAGLIA

DOCUMENTA MATHEMATICA

UNIV BIELEFELD

Año: 2014 vol. 19 p. 439 - 455

Let G be a group and let KH be homotopy algebraic K-theory. We prove that if G satisfies the rational KH isomorphism conjecture for the group algebra L^1[G] with coefficients in the algebra of trace-class operators in Hilbert space, then it also satisfies the K-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.