Algebraic & Geometric Topology

Idempotent functors that preserve cofiber sequences and split suspensions

Jeffrey Strom

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We show that an f–localization functor Lf commutes with cofiber sequences of (N1)–connected finite complexes if and only if its restriction to the collection of (N1)–connected finite complexes is R–localization for some unital subring R. This leads to a homotopy theoretical characterization of the rationalization functor: the restriction of Lf to simply connected spaces (not just the finite complexes) is rationalization if and only if Lf(S2) is nontrivial and simply connected, Lf preserves cofiber sequences of simply connected finite complexes and for each simply connected finite complex K, there is a k such that ΣkLf(K) splits as a wedge of copies of Lf(Sn) for various values of n.

Article information

Algebr. Geom. Topol., Volume 13, Number 4 (2013), 2335-2346.

Received: 21 October 2012
Revised: 15 February 2013
Accepted: 18 February 2013
First available in Project Euclid: 19 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P60: Localization and completion 55P62: Rational homotopy theory
Secondary: 55P35: Loop spaces 55P40: Suspensions

localization rationalization suspension


Strom, Jeffrey. Idempotent functors that preserve cofiber sequences and split suspensions. Algebr. Geom. Topol. 13 (2013), no. 4, 2335--2346. doi:10.2140/agt.2013.13.2335.

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