Co-H-spaces and the Ganea conjecture

Research output: Contribution to journalArticle

3 Citations (Scopus)

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→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.

Original languageEnglish
Pages (from-to)223-234
Number of pages12
JournalTopology
Volume40
Issue number2
DOIs
Publication statusPublished - Mar 1 2001

Fingerprint

H-space
Coaction
Homotopy
Homology
Circle
Decompose
Series

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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

In: Topology, Vol. 40, No. 2, 01.03.2001, p. 223-234.

Research output: Contribution to journalArticle

Iwase, Norio. / Co-H-spaces and the Ganea conjecture. In: Topology. 2001 ; Vol. 40, No. 2. pp. 223-234.
@article{6bb56ea368ca409781293aa7ca44f739,
title = "Co-H-spaces and the Ganea conjecture",
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→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.",
author = "Norio Iwase",
year = "2001",
month = "3",
day = "1",
doi = "10.1016/S0040-9383(99)00052-X",
language = "English",
volume = "40",
pages = "223--234",
journal = "Topology",
issn = "0040-9383",
publisher = "Elsevier Limited",
number = "2",

}

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 -