Geodesic
Idempotent functors that preserve cofiber sequences and split suspensions
Strom, Jeffrey1
1Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, MI 49008, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2335-2346
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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 ⊆ ℚ. 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.

DOI : 10.2140/agt.2013.13.2335
Classification : 55P60, 55P62, 55P35, 55P40
Keywords: localization, rationalization, suspension

Strom, Jeffrey  1

1 Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, MI 49008, USA 
@article{10_2140_agt_2013_13_2335,
     author = {Strom, Jeffrey},
     title = {Idempotent functors that preserve cofiber sequences and split suspensions},
     journal = {Algebraic and Geometric Topology},
     pages = {2335--2346},
     year = {2013},
     volume = {13},
     number = {4},
     doi = {10.2140/agt.2013.13.2335},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.2335/}
}
TY  - JOUR
AU  - Strom, Jeffrey
TI  - Idempotent functors that preserve cofiber sequences and split suspensions
JO  - Algebraic and Geometric Topology
PY  - 2013
SP  - 2335
EP  - 2346
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.2335/
DO  - 10.2140/agt.2013.13.2335
ID  - 10_2140_agt_2013_13_2335
ER  - 
%0 Journal Article
%A Strom, Jeffrey
%T Idempotent functors that preserve cofiber sequences and split suspensions
%J Algebraic and Geometric Topology
%D 2013
%P 2335-2346
%V 13
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.2335/
%R 10.2140/agt.2013.13.2335
%F 10_2140_agt_2013_13_2335
Strom, Jeffrey. Idempotent functors that preserve cofiber sequences and split suspensions. Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2335-2346. doi: 10.2140/agt.2013.13.2335

[1] A K Bousfield, D M Kan, The core of a ring, J. Pure Appl. Algebra 2 (1972) 73

[2] C Casacuberta, D Scevenels, J H Smith, Implications of large-cardinal principles in homotopical localization, Adv. Math. 197 (2005) 120

[3] E D Farjoun, Cellular spaces, null spaces and homotopy localization, Lecture Notes in Mathematics 1622, Springer (1996)

[4] Y Félix, S Halperin, Rational LS category and its applications, Trans. Amer. Math. Soc. 273 (1982) 1

[5] Y Félix, J M Lemaire, On the mapping theorem for Lusternik–Schnirelmann category, Topology 24 (1985) 41

[6] D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205

[7] J Strom, Finite-dimensional spaces in resolving classes, Fund. Math. 217 (2012) 171

[8] D Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. 100 (1974) 1

Cité par Sources :