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)

 
 

 

A topological note on the Adams spectral sequence based on Morava's $ K$-theory


Author: Nobuaki Yagita
Journal: Proc. Amer. Math. Soc. 72 (1978), 613-617
MSC: Primary 55N22
DOI: https://doi.org/10.1090/S0002-9939-1978-0509264-5
MathSciNet review: 509264
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we compute the Hopf algebra $ K{(n)_ \ast}(K(n))$ and consider the Adams spectral sequence of $ K{(n)_ \ast}( - )$ theory.


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

  • [1] J. F. Adams, Stable homotopy and generalised homology, Univ. Chicago Press, Chicago, Ill., 1974. MR 0402720 (53:6534)
  • [2] D. C. Johnson and W. S. Wilson, BP operations and Morava's extraordinary K-theories, Math. Z. 144 (1975), 55-75. MR 0377856 (51:14025)
  • [3] H. R. Miller and D. C. Ravenel, Morava stabilizer algebras and the localization of Novikov's $ {E_2}$-term, Duke Math. J. 44 (1977), 433-447. MR 0458410 (56:16613)
  • [4] H. R. Miller, D. C. Ravenel and W. S. Wilson, Novikov's $ {\operatorname{Ext}^2}$ and the nontriviality of the gamma family, Bull. Amer. Math. Soc. 81 (1975), 1073-1075. MR 0380790 (52:1687)
  • [5] J. Morava, Structure theorems for cobordism comodules (to appear).
  • [6] D. C. Ravenel, The structure of Morava stabilizer algebras, Invent. Math. 37 (1976), 109-120. MR 0420619 (54:8632)
  • [7] N. Shimada and N. Yagita, Multiplications in the complex bordism theory with singularities, Publ. RIMS, Kyoto Univ. 12 (1976), 259-293. MR 0415642 (54:3723)
  • [8] L. Smith, On realizing complex cobordism modules. Amer. J. Math. 92 (1970), 793-856. MR 0275429 (43:1186a)
  • [9] N. Yagita, On the algebraic structure of cobordism operations with singularities, J. London Math. Soc. 16 (1977), 131-141. MR 0445492 (56:3832)
  • [10] J. Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 250-271. MR 0099653 (20:6092)
  • [11] N. Yagita, The exact functor theorem for $ {\text{BP}_ \ast}/{I_n}$-theory, Proc. Japan Acad. 52 (1976), 1-3. MR 0394631 (52:15432)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55N22

Retrieve articles in all journals with MSC: 55N22


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0509264-5
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society