The Selected Works of J. Frank Adams 2 Volume Set

Erscheinungsjahr 2010
ISBN: 978-0-521-18214-0
Verlag: Cambridge University Press

Buch, Englisch, 1097 Seiten, Format (B × H): 191 mm x 249 mm, Gewicht: 1996 g

J. Frank Adams, one of the world's leading topologists, solved a number of celebrated problems in algebraic topology, a subject in which he initiated many of the most active areas of research. His papers written between 1955 and 1988, few of which have been superseded, are characterised by elegant writing and depth of thought. These two 1992 volumes contain all his major research contributions. The first contains papers on: the cobar construction, the Adams spectral sequence, higher-order cohomology operations, and the Hopf invariant one problem, amongst other topics. The second volume is mainly concerned with Adams' contributions to: characteristic classes and calculations in K-theory; modules over the Steenrod algebra and their Ext groups; finite H-spaces and compact Lie groups; and maps between classifying spaces of compact groups. Anyone interested in algebraic topology will want to own a copy of these volumes as a historical record and a source of reference.

Autoren/Hrsg.

Thomas, Charles B

May, J Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik

Inhaltsverzeichnis

Volume 1: 1. On the chain algebra of a loop space; 2. On the cobar construction; 3. The structure of the Steenrod algebra; 4. On the non-existence theory of elements of Hopf invariant one; 4. Applications of the Groethendieck–Atiyah–Hirzebruch functor K(X); 5. Vector fields on spheres; 6. On complex Stiefel manifolds; 7. On matrices whose real linear combinations are non-singular and correction; 8. On the groups J(X) I, II, III, and IV and correction; 9. K-theory and the Hopf invariant; 10. Geometric dimension of bundles over RPn; 11. Lectures on generalised cohomology; 12. Algebraic topology in the last decade. Volume 2: 1. On formulae of Thom and Wu; 2. On Chern characters and the structure of the unitary group; 3. Chern characters revisited and the structure of the unitary group; 4. Chern characters revisited and addendum; 5. The Hurewicz homomorphism for MU and BP; 6. Hopf algebras of co-operators for real and complex K-theory; 7. Operations of the Nth kind in K-theory; 8. Operations on K-theory of torsion-free spaces; 9. Stable operations on complex K-theory; 10. Primitive elements in the K-theory of BSU; 11. A finiteness theorem in homological algebra; 12. A periodicity theorem in homological algebra; 13. Modules over the Steenrod algebra; 14. Sub-Hopf-algebras of the Steenrod algebra; 15. What we don't know about RP8; 16. Calculations of Lin's Ext groups; 17. The Segal conjecture for elementary abelian p-groups; 18. The sphere considered as an H-space mod p; 19. H-spaces with few cells; 20. Finite H-spaces and Lie groups; 21. Spin(8) triality, F4 and all that; 22. The fundamental representations of E8; 23. 2-tori in E8; Maps between classifying spaces I, II, and III; 24. Maps between p-completed classifying spaces; 25. An example in homotopy theory; 26. A variant of E. H. Brown's representability theorem; 27. Idempotent functors in homotopy theory; 28. The Kahn–Priddy theorem; 29. Uniquenesss of BSO; 30. Graeme Segal's Burnsides ring conjecture; 31. A generalisation of the Segal conjecture; 32. A generalisation of the Atiyah–Segal completion theorem; 33. Atomic spaces and spectra; 34. Two theorems of J. Lannes; 35. The work of M. J. Hopkins.