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

A topological note on the Adams spectral sequence based on Morava’s $K$-theory
HTML articles powered by AMS MathViewer

by Nobuaki Yagita PDF

Proc. Amer. Math. Soc. 72 (1978), 613-617 Request permission

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

J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0402720
David Copeland Johnson and W. Stephen Wilson, $BP$ operations and Morava’s extraordinary $K$-theories, Math. Z. 144 (1975), no. 1, 55–75. MR 377856, DOI 10.1007/BF01214408
Haynes R. Miller and Douglas C. Ravenel, Morava stabilizer algebras and the localization of Novikov’s $E_{2}$-term, Duke Math. J. 44 (1977), no. 2, 433–447. MR 458410
Haynes R. Miller, Douglas C. Ravenel, and W. Stephen Wilson, Novikov’s $\textrm {Ext}^{2}$ and the nontriviality of the gamma family, Bull. Amer. Math. Soc. 81 (1975), no. 6, 1073–1075. MR 380790, DOI 10.1090/S0002-9904-1975-13921-8

Structure theorems for cobordism comodules

Douglas C. Ravenel, The structure of Morava stabilizer algebras, Invent. Math. 37 (1976), no. 2, 109–120. MR 420619, DOI 10.1007/BF01418965
Nobuo Shimada and Nobuaki Yagita, Multiplications in the complex bordism theory with singularities, Publ. Res. Inst. Math. Sci. 12 (1976/77), no. 1, 259–293. MR 0415642, DOI 10.2977/prims/1195190968
Larry Smith, On realizing complex bordism modules. Applications to the stable homotopy of spheres, Amer. J. Math. 92 (1970), 793–856. MR 275429, DOI 10.2307/2373397
Nobuaki Yagita, On the algebraic structure of cobordism operations with singularities, J. London Math. Soc. (2) 16 (1977), no. 1, 131–141. MR 445492, DOI 10.1112/jlms/s2-16.1.131
John Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150–171. MR 99653, DOI 10.2307/1969932
Nobuaki Yagita, The exact functor theorem for $\textrm {BP}_\ast /I_{n}$-theory, Proc. Japan Acad. 52 (1976), no. 1, 1–3. MR 394631