### 抄録

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.

元の言語 | 英語 |
---|---|

ページ（範囲） | 223-234 |

ページ数 | 12 |

ジャーナル | Topology |

巻 | 40 |

発行部数 | 2 |

DOI | |

出版物ステータス | 出版済み - 3 1 2001 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### これを引用

*Topology*,

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

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

研究成果: ジャーナルへの寄稿 › 記事

*Topology*, 巻. 40, 番号 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

VL - 40

SP - 223

EP - 234

JO - Topology

JF - Topology

SN - 0040-9383

IS - 2

ER -