Baumslag rationalization of spaces

TL;DR

This paper introduces a new functor called Baumslag rationalization for all spaces, extending classical rationalization, and compares it with other existing rationalization methods.

Contribution

It constructs and analyzes a novel rationalization functor for spaces that generalizes classical rationalization to non-simply connected spaces.

Findings

The Baumslag rationalization functor extends classical rationalization to broader classes of spaces.

Comparison with other rationalization methods highlights differences and similarities.

The new functor provides a unified framework for understanding rationalization in algebraic topology.

Abstract

Using the functor of Baumslag rationalization of groups we construct a functor on the category of all (non necessarily simply connected) spaces that extends the classical rationalization of simply connected spaces. We study this functor and compare it with other extensions of the classical rationalization: Bousfield-Kan $\mathbb Q$-completion; Bousfield's homology rationalization; G\'{o}mez-Tato--Halperin--Tantr\'{e}'s $\pi_1$-fiberwise rationalization; and the localization with respect to the maps $n:S^1\to S^1$ that we call $\Omega$-rationalization.