A Classification Theorem for Homotopy Commutative H-Spaces with Finitely Generated Mod 2 Cohomology Rings (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Slack, Michael

Softcover

ISBN 10: 0821825143 ISBN 13: 9780821825143

Publisher: American Mathematical Society, 1992

Synopsis

Many homological properties of Lie groups are derived strictly from homotopy-theoretic considerations and do not depend on any geometric or analytic structure. An H-space is a topological space having a continuous multiplication with unit. Generalizing from Lie group theory, John Hubbuck proved that a connected, homotopy commutative H-space which is a finite cell complex has the homotopy type of a torus. There are many interesting examples of H-spaces which are not finite
complexes - loop spaces are one example.

The aim of this book is to prove a version of Hubbuck's theorem in which the condition that the H-space be a finite cell complex is replaced by the condition that it have a finitely-generated mod 2 cohomology ring. The conclusion of the theorem is slightly more general in this case, and some mild associativity hypotheses are required. The method of proof uses established techniques in H-space theory, as well as a new obstruction-theoretic approach to (Araki-Kudo-Dyer-Lashof) homology
operations for iterated loop spaces.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1992
• Language: English
• ISBN 10: 0821825143
• ISBN 13: 9780821825143
• Binding: Paperback