An Analytic Novikov Conjecture for Semigroups

TL;DR

This paper extends the analytic Novikov conjecture to semigroups, demonstrating that techniques from coarse geometry can be adapted to this broader algebraic context.

Contribution

It introduces a new formulation of the analytic Novikov conjecture for semigroups and shows the descent argument from coarse geometry applies to this setting.

Findings

The descent argument from coarse geometry generalizes to semigroups.

A new version of the analytic Novikov conjecture for semigroups is formulated.

The approach broadens the applicability of the conjecture to algebraic structures beyond groups.

Abstract

In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.