Grbić, Jelena
(2006)
*Universal homotopy associative, homotopy commutative $H$-spaces and the EHP spectral sequence.*
Mathematical Proceedings of the Cambridge Philosophical Society, 140 (3).
pp. 377-400.
ISSN 0305-0041

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## 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 $f\colon X\to Y$ to a homotopy associative, homotopy commutative $H$-space extends to a uniquely determined $H$-map $\overline{f}\colon U(X)\to Y$. 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.

Item Type: | Article |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 13 Commutative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 52 Convex and discrete geometry MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 19 Nov 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/917 |

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