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Proceedings of the London Mathematical Society Advance Access published online on June 13, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn029
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© 2008 London Mathematical Society

The orbit space of a fusion system is contractible

Markus Linckelmann

Department of Mathematical Sciences
University of Aberdeen
Meston Building
Aberdeen
AB24 3UE
United Kingdom

Received 30 May 2006. Revision received 10 April 2008.

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].

2000 Mathematics Subject Classification 55U15.


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