A Classification Theorem for Homotopy Commutative H-Spaces With Finitely Generated Mod 2 Cohomology Rings - Brossura

Slack, Michael

Brossura

ISBN 10: 0821825143 ISBN 13: 9780821825143

Casa editrice: Amer Mathematical Society, 1991

Riassunto

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.

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Contenuti

Techniques used in the proof; Initial study of QHeven, initial study QHodd, Further study of QH*; QH* in low degrees; Proof of corollaries.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 0821825143
• ISBN 13: 9780821825143
• Rilegatura: Copertina flessibile
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile