On rational injectivity of Kasparovs assembly map in dimension <=2

2012/10/08 by Ulrich Haag, Haag, Ulrich
Mathematics · #19K35 (Primary) 55P15 (Secondary) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:19K35 #msc:55P15

paper · pdf · doi:10.48550/arxiv.1210.2303

16 pages

arxiv created 2012/10/08 · arxiv updated 2012/10/09

Abstract

The author presents a new proof of injectivity of the composition of the inverse of the rational Chern Character in homology applied to the classifying space BG of a (countable) discrete group G, restricted to dimensions less or equal than two, with the rationalized Assembly map of Kasparov into the (operator) K-Theory of the full group C^*-algebra C^*(G) (tensored with the rational numbers).

Related

• The Chern-Connes character is not rationally injective
• Trace class operators, regulators, and assembly maps in K-theory
• Polynomially bounded cohomology and the Novikov Conjecture
• The strong Novikov conjecture for low degree cohomology
• C*-categories, Groupoid Actions, Equivariant KK-theory, and the Baum-Connes Conjecture