A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $\bmod 2$ Cohomology Rings

Download or read book A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $\bmod 2$ Cohomology Rings written by Michael Slack and published by American Mathematical Soc.. This book was released on 1991 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that a 2-connected homotopy commutative H-space with associative mod 2 homology ring and finitely generated mod 2 cohomology ring has acyclic mod 2 cohomology. This implies that a connected, homotopy commutative, homotopy associative H-space with finitely generated mod 2 cohomology ring is mod 2 homotopy equivalent to a product of Eilenberg-MacLane spaces, giving a complete classification of such spaces localized at the prime 2.