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A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $/Bmod 2$ Cohomology Rings
1991
American Mathematical Society (Verlag)
978-0-8218-2514-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2514-3 (ISBN)
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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.
Erscheint lt. Verlag | 30.8.1991 |
---|---|
Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik |
Schlagworte | Memoirs of the AMS; No. 449 |
ISBN-10 | 0-8218-2514-3 / 0821825143 |
ISBN-13 | 978-0-8218-2514-3 / 9780821825143 |
Zustand | Neuware |
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