Higher limits over the fusion orbit category via centralizers of amalgams

2024/11/02 by Bova, Marco Praderio
#20C99 #20D20 #20J05 #55T99 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.01352

Abstract

We study the Díaz-Park sharpness conjecture for fusion systems and prove that, under certain circumstances, there exists a 4 terms exact sequence relating the first two higher limits of the contravariant part of a Mackey functor over certain fusion systems. We show how this result can be applied to the family of Benson-Solomon fusion systems thus providing another approach to studying the sharpness for this family of fusion systems.

Related

• Sharpness for the Benson-Solomon fusion systems
• Mackey functors and sharpness for fusion systems
• Sharpness of saturated fusion systems on a Sylow p-subgroup of \rm G₂(p)
• Mislin's theorem for fusion systems via Mackey functors
• Cohomology on the centric orbit category of a fusion system