On generalized plus-constructions of Eilenberg–Mac Lane spaces

✍ Scribed by Jin-Yen Tai

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 144 KB
• Volume: 106
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00084-x

✦ Synopsis

A GEM is an infinite loop space which is weakly equivalent to a product of Eilenberg-Mac Lane spaces. In this paper, the fiber of any f -localization map of a GEM is shown to be a GEM again. Using this result, we compute explicitly the p-local and p-torsion generalized plus-constructions of abelian Eilenberg-Mac Lane spaces. We also prove some arithmetic square results to compute the generalized plus-construction of Eilenberg-Mac Lane spaces in general.