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Idempotent functors that preserve cofiber sequences and split suspensions

Jeffrey Strom

Algebraic & Geometric Topology 13 (2013) 2335–2346

We show that an f–localization functor Lf commutes with cofiber sequences of (N 1)–connected finite complexes if and only if its restriction to the collection of (N 1)–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.

localization, rationalization, suspension
Mathematical Subject Classification 2010
Primary: 55P60, 55P62
Secondary: 55P35, 55P40
Received: 21 October 2012
Revised: 15 February 2013
Accepted: 18 February 2013
Published: 30 June 2013
Jeffrey Strom
Department of Mathematics
Western Michigan University
1903 W. Michigan Ave.
Kalamazoo, MI 49008