### Abstract

A non-simply connected co-H-space X is, up to homotopy, the total space of a fibrewise-simply connected pointed fibrewise co-Hopf fibrant j:X→Bπ_{1}(X), which is a space with a co-action of Bπ_{1}(X) along j. We construct its homology decomposition, which yields a simple construction of its fibrewise localisation. Our main result is the construction of a series of co-H-spaces, each of which cannot be split into a one-point-sum of a simply connected space and a bunch of circles, thus disproving the Ganea conjecture.

Original language | English |
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Pages (from-to) | 223-234 |

Number of pages | 12 |

Journal | Topology |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

*Topology*,

*40*(2), 223-234. https://doi.org/10.1016/S0040-9383(99)00052-X

**Co-H-spaces and the Ganea conjecture.** / Iwase, Norio.

Research output: Contribution to journal › Article

*Topology*, vol. 40, no. 2, pp. 223-234. https://doi.org/10.1016/S0040-9383(99)00052-X

}

TY - JOUR

T1 - Co-H-spaces and the Ganea conjecture

AU - Iwase, Norio

PY - 2001/3/1

Y1 - 2001/3/1

N2 - A non-simply connected co-H-space X is, up to homotopy, the total space of a fibrewise-simply connected pointed fibrewise co-Hopf fibrant j:X→Bπ1(X), which is a space with a co-action of Bπ1(X) along j. We construct its homology decomposition, which yields a simple construction of its fibrewise localisation. Our main result is the construction of a series of co-H-spaces, each of which cannot be split into a one-point-sum of a simply connected space and a bunch of circles, thus disproving the Ganea conjecture.

AB - A non-simply connected co-H-space X is, up to homotopy, the total space of a fibrewise-simply connected pointed fibrewise co-Hopf fibrant j:X→Bπ1(X), which is a space with a co-action of Bπ1(X) along j. We construct its homology decomposition, which yields a simple construction of its fibrewise localisation. Our main result is the construction of a series of co-H-spaces, each of which cannot be split into a one-point-sum of a simply connected space and a bunch of circles, thus disproving the Ganea conjecture.

UR - http://www.scopus.com/inward/record.url?scp=0043194099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043194099&partnerID=8YFLogxK

U2 - 10.1016/S0040-9383(99)00052-X

DO - 10.1016/S0040-9383(99)00052-X

M3 - Article

AN - SCOPUS:0043194099

VL - 40

SP - 223

EP - 234

JO - Topology

JF - Topology

SN - 0040-9383

IS - 2

ER -