Filtrations of simplicial functors and the Novikov Conjecture

TL;DR

This paper links the Strong Novikov Conjecture to topological K-theory, demonstrating equivalences and implications for rational injectivity of assembly maps in the context of discrete groups and their C*-algebras.

Contribution

It establishes an equivalence between the Strong Novikov Conjecture and a topological K-theory statement, and relates rational injectivity of assembly maps in topological and algebraic K-theory.

Findings

Strong Novikov Conjecture is equivalent to a topological K-theory statement.

Rational injectivity of the full assembly map follows from the restricted one.

The results connect algebraic and topological K-theory in the context of discrete groups.

Abstract

We show that the Strong Novikov Conjecture for the maximal C*-algebra C*(G) of a discrete group G is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group G, rational injectivity of the full assembly map for the topological K-theory of C*(G) follows from rational injectivity of the restricted assembly map.