Buch, Englisch, 116 Seiten, Format (B × H): 180 mm x 255 mm
Buch, Englisch, 116 Seiten, Format (B × H): 180 mm x 255 mm
ISBN: 978-0-8218-2514-3
Verlag: American Mathematical Society
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.
Autoren/Hrsg.
Weitere Infos & Material
Techniques used in the proof; Initial study of QHeven, initial study QHodd, Further study of QH*; QH* in low degrees; Proof of corollaries.
