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

TL;DR

This paper provides a new proof demonstrating the rational injectivity of Kasparov's assembly map in low dimensions (<=2), linking homology and operator K-theory for discrete groups.

Contribution

It introduces a novel proof of the rational injectivity of Kasparov's assembly map in dimensions up to two, enhancing understanding of the Baum-Connes conjecture in low dimensions.

Findings

Proof of rational injectivity in dimensions <=2

Connections between homology and operator K-theory

Advancement in understanding the Baum-Connes conjecture

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).