### Abstract

Assume that all spaces and maps are localised at a fixed prime p. We study the possibility of generating a universal space U(X) from a space X which is universal in the category of homotopy associative, homotopy commutative H-spaces in the sense that any map f: X -> Y to a homotopy associative, homotopy commutative H-space extends to a uniquely determined H-map (f) over bar: U(X) -> Y. Developing a method for recognising certain universal spaces, we show the existence of the universal space F-2(n) of a certain three-cell complex L. Using this specific example: we derive some consequences for the calculation of the unstable homotopy groups of spheres, namely we obtain a formula, for the d(1)-differential of the EHP-spectral sequence valid in a certain range.

Original language | English |
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Pages (from-to) | 377-400 |

Number of pages | 23 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 140 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- DOUBLE SUSPENSION

### Cite this

**Universal homotopy associative, homotopy commutative H-spaces and the EHP spectral sequence.** / Grbic, Jelena.

Research output: Contribution to journal › Article

*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 140, no. 3, pp. 377-400. https://doi.org/10.1017/S0305004106009182

}

TY - JOUR

T1 - Universal homotopy associative, homotopy commutative H-spaces and the EHP spectral sequence

AU - Grbic, Jelena

PY - 2006

Y1 - 2006

N2 - Assume that all spaces and maps are localised at a fixed prime p. We study the possibility of generating a universal space U(X) from a space X which is universal in the category of homotopy associative, homotopy commutative H-spaces in the sense that any map f: X -> Y to a homotopy associative, homotopy commutative H-space extends to a uniquely determined H-map (f) over bar: U(X) -> Y. Developing a method for recognising certain universal spaces, we show the existence of the universal space F-2(n) of a certain three-cell complex L. Using this specific example: we derive some consequences for the calculation of the unstable homotopy groups of spheres, namely we obtain a formula, for the d(1)-differential of the EHP-spectral sequence valid in a certain range.

AB - Assume that all spaces and maps are localised at a fixed prime p. We study the possibility of generating a universal space U(X) from a space X which is universal in the category of homotopy associative, homotopy commutative H-spaces in the sense that any map f: X -> Y to a homotopy associative, homotopy commutative H-space extends to a uniquely determined H-map (f) over bar: U(X) -> Y. Developing a method for recognising certain universal spaces, we show the existence of the universal space F-2(n) of a certain three-cell complex L. Using this specific example: we derive some consequences for the calculation of the unstable homotopy groups of spheres, namely we obtain a formula, for the d(1)-differential of the EHP-spectral sequence valid in a certain range.

KW - DOUBLE SUSPENSION

U2 - 10.1017/S0305004106009182

DO - 10.1017/S0305004106009182

M3 - Article

VL - 140

SP - 377

EP - 400

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -