## The functor A min on p-local spaces

Citations: | 9 - 8 self |

### BibTeX

@MISC{Selick_thefunctor,

author = {Paul Selick and Jie Wu},

title = {The functor A min on p-local spaces},

year = {}

}

### OpenURL

### Abstract

Abstract. In a previous paper, the authors gave the finest functorial decomposition of the loop suspension of a p-torsion suspension. The purpose of this paper is to generalize this theorem to arbitrary p-local path connected spaces. 1.

### Citations

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(Show Context)
Citation Context ...te. Let C be a pointed filtered coalgebra and let A be a filtered Hopf algebra. We write [C, A] for the set of pointed filtered coalgebra morphisms from C to A. By Lemma 3.1, we have Proposition 3.2. =-=[11]-=- Let C be a connected filtered coalgebra and let A be a connected Hopf algebra. Then [C, A] is a group under the convolution multiplication. Let C be a filtered coalgebra. Then E 0 ∞� C = s=0 I s C/I ... |

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(Show Context)
Citation Context ...a functorial isomorphism of coalgebras Gr H∗(A min (X)) ∼ = A min ( ¯ H∗(X)). Note: 1) The Adams spectral sequence can be obtained by considering the descending central series of Kan’s G-construction =-=[1, 2, 7, 10, 14]-=-. Theorem 1.2 gives a decomposition of the Adams spectral sequence for π∗(ΣX). Theorem 1.1 shows that the sub spectral sequence corresponding to π∗(A min (X)) is accelerated. 2) Functorial decompositi... |

55 |
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Citation Context ...r π∗(ΣX). Theorem 1.1 shows that the sub spectral sequence corresponding to π∗(A min (X)) is accelerated. 2) Functorial decompositions of ΩΣX have been studied in several references. (See for example =-=[3, 4, 6, 15]-=-.) Theorem 1.2 is a generalization of the results given in [12].sTHE FUNCTOR A min ON p-LOCAL SPACES 3 The idea of the proof is to define a specific map πX (see Section 2) and show that ΩπX has a left... |

43 |
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(Show Context)
Citation Context ...a functorial isomorphism of coalgebras Gr H∗(A min (X)) ∼ = A min ( ¯ H∗(X)). Note: 1) The Adams spectral sequence can be obtained by considering the descending central series of Kan’s G-construction =-=[1, 2, 7, 10, 14]-=-. Theorem 1.2 gives a decomposition of the Adams spectral sequence for π∗(ΣX). Theorem 1.1 shows that the sub spectral sequence corresponding to π∗(A min (X)) is accelerated. 2) Functorial decompositi... |

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(Show Context)
Citation Context ...a functorial isomorphism of coalgebras Gr H∗(A min (X)) ∼ = A min ( ¯ H∗(X)). Note: 1) The Adams spectral sequence can be obtained by considering the descending central series of Kan’s G-construction =-=[1, 2, 7, 10, 14]-=-. Theorem 1.2 gives a decomposition of the Adams spectral sequence for π∗(ΣX). Theorem 1.1 shows that the sub spectral sequence corresponding to π∗(A min (X)) is accelerated. 2) Functorial decompositi... |

24 |
On natural decompositions of loop suspensions and natural coalgebra decompositions of tensor algebras
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(Show Context)
Citation Context .... The purpose of this paper is to generalize this theorem to arbitrary p-local path connected spaces. 1. Introduction Functorial decompositions of ΩΣX for p-torsion suspensions X have been studied in =-=[12]-=-. The most important factor is the “smallest” functorial homotopy retract of ΩΣX which contains the homology of X. This factor was denoted by A min (X). The purpose of this paper is to eliminate the h... |

21 |
On combinatorial group theory in homotopy, Contemp
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(Show Context)
Citation Context ...r π∗(ΣX). Theorem 1.1 shows that the sub spectral sequence corresponding to π∗(A min (X)) is accelerated. 2) Functorial decompositions of ΩΣX have been studied in several references. (See for example =-=[3, 4, 6, 15]-=-.) Theorem 1.2 is a generalization of the results given in [12].sTHE FUNCTOR A min ON p-LOCAL SPACES 3 The idea of the proof is to define a specific map πX (see Section 2) and show that ΩπX has a left... |

16 |
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- 1998
(Show Context)
Citation Context ...r π∗(ΣX). Theorem 1.1 shows that the sub spectral sequence corresponding to π∗(A min (X)) is accelerated. 2) Functorial decompositions of ΩΣX have been studied in several references. (See for example =-=[3, 4, 6, 15]-=-.) Theorem 1.2 is a generalization of the results given in [12].sTHE FUNCTOR A min ON p-LOCAL SPACES 3 The idea of the proof is to define a specific map πX (see Section 2) and show that ΩπX has a left... |

13 |
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