Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A relation between $ K$-theory and cohomology


Author: Alan Thomas
Journal: Trans. Amer. Math. Soc. 193 (1974), 133-142
MSC: Primary 55G25
DOI: https://doi.org/10.1090/S0002-9947-1974-0370584-X
MathSciNet review: 0370584
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that for X a CW-complex, $ K(X)$ and $ {H^{{\text{ev}}}}(X)$ are isomorphic modulo finite groups, although the ``isomorphism'' is not natural. The purpose of this paper is to improve this result for X a finite CW-complex.


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

  • [1] M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., vol. 3, Amer. Math. Soc., Providence, R. I., 1961, pp. 7-38. MR 25 #2617. MR 0139181 (25:2617)
  • [2] M. F. Atiyah and D. O. Tall, Group representations, $ \lambda $-rings and the J -homomorphism, Topology 8 (1969), 253-297. MR 39 #5702. MR 0244387 (39:5702)
  • [3] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergebnisse der Math. und ihrer Grenzgebiete, Heft 9, Springer-Verlag, Berlin, 1956; English transl., Die Grundlehren der math. Wissenschaften, Band 131, Springer-Verlag, New York, 1966. MR 18, 509; 34 #2573. MR 0082174 (18:509b)
  • [4] A. Dold, Halbexakte homotopiefunktoren, Lecture Notes in Math., vol. 12, Springer-Verlag, Berlin and New York, 1966. MR 33 #6622. MR 0198464 (33:6622)
  • [5] A. Borel and F. Hirzebnich, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538. MR 21 #1586. MR 0102800 (21:1586)
  • [6] L. Hodgkin, On the K-theory of Lie groups, Topology 6 (1967), 1-36. MR 35 #4950. MR 0214099 (35:4950)
  • [7] F. Peterson, Some remarks on Chern classes, Ann. of Math. (2) 69 (1959), 414-420. MR 21 #1593. MR 0102807 (21:1593)
  • [8] E. H. Brown, Cohomology theories, Ann. of Math (2)75 (1962), 467-484. MR 25 #1551. MR 0138104 (25:1551)
  • [9] J. P. Serre, Groupes d'homotopie et classes de groups abéliens, Ann. of Math. (2) 58 (1953), 258-294. MR 15, 548. MR 0059548 (15:548c)
  • [10] A. Grothendieck, Special $ \lambda $-rings, (1957) (unpublished).
  • [11] A. Thomas, Almost complex structures on complex projective spaces, Trans. Amer. Math. Soc. 193 (1974), 123-132. MR 0353196 (50:5681)
  • [12] D. Knutson, $ \lambda $ rings and the representation theory of the symmetric group, Lecture Notes in Math., vol. 308, Springer-Verlag, Berlin and New York, 1973. MR 0364425 (51:679)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55G25

Retrieve articles in all journals with MSC: 55G25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0370584-X
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society