### Abstract

Original language | English |
---|---|

Pages (from-to) | 191-216 |

Number of pages | 26 |

Journal | Journal of the London Mathematical Society |

Volume | 98 |

Issue number | 1 |

Early online date | 13 Jun 2008 |

DOIs | |

Publication status | Published - Jan 2009 |

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### Cite this

*Journal of the London Mathematical Society*,

*98*(1), 191-216. https://doi.org/10.1112/plms/pdn029

**The orbit space of a fusion system is contractible.** / Linckelmann, Markus.

Research output: Contribution to journal › Article

*Journal of the London Mathematical Society*, vol. 98, no. 1, pp. 191-216. https://doi.org/10.1112/plms/pdn029

}

TY - JOUR

T1 - The orbit space of a fusion system is contractible

AU - Linckelmann, Markus

PY - 2009/1

Y1 - 2009/1

N2 - Given a fusion system F on a finite p-group P, where p is a prime, we show that the partially ordered set of isomorphism classes in F of chains of non-trivial subgroups of P, considered as topological space, is contractible, further generalising Symonds’, proof [Comment. Math. Helvet. 73 (1998) 400–405] of a conjecture of Webb [Comment. Math. Helvet. 66 (1991) 34–69; Arcata Conference on Representations of Finite Groups, part I, Proceedings of Symposia in Pure Mathematics 47 349–365] and its generalisation to non-trivial Brauer pairs associated with a p-block by Barker [J. Algebra 212 (1999) 460–465].

AB - Given a fusion system F on a finite p-group P, where p is a prime, we show that the partially ordered set of isomorphism classes in F of chains of non-trivial subgroups of P, considered as topological space, is contractible, further generalising Symonds’, proof [Comment. Math. Helvet. 73 (1998) 400–405] of a conjecture of Webb [Comment. Math. Helvet. 66 (1991) 34–69; Arcata Conference on Representations of Finite Groups, part I, Proceedings of Symposia in Pure Mathematics 47 349–365] and its generalisation to non-trivial Brauer pairs associated with a p-block by Barker [J. Algebra 212 (1999) 460–465].

U2 - 10.1112/plms/pdn029

DO - 10.1112/plms/pdn029

M3 - Article

VL - 98

SP - 191

EP - 216

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -