The homotopy theory of fusion systems

By C. Broto, Ran Levi, B. Oliver. 2003

339 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0b3c1a5a21987eb4336ba9c9b3227cfecfaa6011

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Citations in the corpus

Extensions of linking systems with p-group kernel (2007, background): “Abstract fusion and linking systems have also been defined and studied, and are shown in [ 5 ] to have many of the same properties as the fusion and linking systems of finite groups.”
The classification of p-local finite groups over the extraspecial group of order p3 and exponent p (2004, background): “In this section we quickly review the concept of a p-local finite group introduced in [2] that builds on previous unpublished work of Ll.”
Reduced, tame and exotic fusion systems (2010, methodology): “up and hence itself a group. Another proof of this, as well as a proof that AutI typ(L) is a group, will be given in Lemma 1.14. 10 KASPERANDERSEN,BOBOLIVER,ANDJOANAVENTURA One of the main results in [BLO2] (Theorem 8.1) says that for any p-local ﬁnite group (S,F,L), Outtyp(L) ∼= Out(|L|∧ p): the gr”
CONTROL OF FUSION IN FUSION SYSTEMS (2006, background): “Oliver [ BLO ] had a dierent definition of the fusion systems which they have proved to be equivalent to Puig’s definition.”
Construction of 2-local finite groups of a type studied by Solomon and Benson (2002, methodology): “ful for constructing saturated fusion systems. This is then followed by a more technical result, which is designed to handle the speciﬁc construction in Section 2. We ﬁrst recall some deﬁnitions from [6]. A fusion system over a p–group Sis a category Fwhose objects are the subgroups of F, such that ”
Discrete models for the p-local homotopy theory of compact Lie groups and p-compact groups (2007, positive): “The new idea here is to replace fusion systems over finite p–groups, as handled in [7], by fusion systems over discrete p–toral groups.”
Simple fusion systems and the Solomon 2-local groups (2006, background): “Levi and Oliver proved in [11, 2.1], that there is actually for any odd prime power q a fusion system FSol(q) on P with the above properties, and that this fusion system is the underlying fusion system of a unique 2-local finite group; we are going to call this the Solomon 2-local finite group Sol(q”
Extension of p-local finite groups (2005, methodology): “TO, N. CASTELLANA, J. GRODAL, R. LEVI, & B. OLIVER 1. A quick review of p-local finite groups We ﬁrst recall the deﬁnitions of a fusion system, and a saturated fusion system, in the form given in [BLO2]. For any group G, and any pair of subgroups H,K≤G, we set NG(H,K) = {x∈G|xHx−1 ≤K}, let cx de”
Subgroup Families Controlling p‐Local Finite Groups (2004, background): “As one example, the original proof in [5] that the fusion systems constructed there are saturated [5, Proposition 9.”
All p-local finite groups of rank two for odd prime p (2004, methodology): “When studying the p-local homotopy theory of classifying spaces of finite groups, Broto-Levi-Oliver [11] introduced the concept of p-local finite group as a p-local analogue of the classical concept of finite group.”