Coarse topology, enlargeability, and essentialness

TL;DR

This paper demonstrates that the fundamental classes of closed enlargeable manifolds have non-trivial images in both rational homology and K-theory, using coarse topology methods independent of the Baum--Connes conjecture.

Contribution

It introduces a novel approach using coarse topology to establish non-triviality of fundamental classes in homology and K-theory without relying on the Baum--Connes conjecture.

Findings

Fundamental classes of closed enlargeable manifolds map non-trivially to rational homology.

They also map non-trivially to the K-theory of reduced C*-algebras.

The proofs are independent of the Baum--Connes conjecture.

Abstract

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras. Our proofs do not depend on the Baum--Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.