Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On $ {\rm Ext}\sb {K\sb *(K)}(\pi\sb *(K)$, $ K\sb *(MU))$

Author: Francis Clarke
Journal: Proc. Amer. Math. Soc. 74 (1979), 156-160
MSC: Primary 55T15; Secondary 55N20
MathSciNet review: 521890
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note a spectral sequence is constructed which is used to prove the existence of elements of nonzero homological degree in $ {\operatorname{Ext}_{{K_ \ast }(K)}}({\pi _ \ast }(K), {K_ \ast }(MU))$. Examples of specific elements in terms of representatives in the cobar construction are given.

References [Enhancements On Off] (What's this?)

  • [1] J. F. Adams, Lectures on generalised cohomology, Category Theory, Homology Theory and their Applications, III (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Three), Springer, Berlin, 1969, pp. 1–138. MR 0251716
  • [2] J. F. Adams, Stable homotopy and generalised homology, University of Chicago Press, Chicago, Ill.-London, 1974. Chicago Lectures in Mathematics. MR 0402720
  • [3] -, Operations of the n-th kind in K-theory, and what we don't know about $ R{P^\infty }$, New Developments in Topology, London Math. Soc. Lecture Notes Ser., no. 11, Cambridge Univ. Press, Cambridge, 1977, pp. 1-9.
  • [4] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
  • [5] S. Cormack, Primitive elements in 𝐾-theory, J. London Math. Soc. (2) 9 (1974/75), 46–48. MR 0407830,
  • [6] S. P. Novikov, Methods of algebraic topology from the point of view of cobordism theory, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 855–951 (Russian). MR 0221509
  • [7] Robert M. Switzer, Algebraic topology—homotopy and homology, Springer-Verlag, New York-Heidelberg, 1975. Die Grundlehren der mathematischen Wissenschaften, Band 212. MR 0385836
  • [8] Raphael Zahler, The Adams-Novikov spectral sequence for the spheres, Ann. of Math. (2) 96 (1972), 480–504. MR 0319197,

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55T15, 55N20

Retrieve articles in all journals with MSC: 55T15, 55N20

Additional Information

Keywords: K-theory, unitary bordism, Adams spectral sequence
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society