The homotopy fiber of profinite completion

✍ Scribed by Joseph Roitberg; Pat Touhey

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 110 KB
• Volume: 103
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00006-1

✦ Synopsis

We show that the basepoint-component of the homotopy fiber of Sullivan's profinite completion map c : Y → Y is always an H -space, provided Y is nilpotent of finite type. This observation allows for a reworking of the completion/rationalization approach to phantom map theory and leads to more direct, transparent proofs of various results in the recent literature on phantom maps.