Classifying Spaces of Sporadic Groups

• Overview of our main results

Exposition of background material

• Review of selected aspects of group cohomology
• Simplicial sets and their equivalence with topological spaces
• Bousfield-Kan completions and homotopy colimits
• Decompositions and ample collections of $p$-subgroups
• 2-local geometries for simple groups

Main results on sporadic groups

• Decompositions for the individual sporadic groups
• Details of proofs for individual groups
• Bibliography
• Index