The complex oriented cohomology of extended powers

in terms of the behaviour of €?*(—) on X. Here Cp is the cyclic group on p elements, ECp a contractible space with free Cp action, and X^ the cartesian product ofp copies of X\ the Cp action on X^ is by permutation of factors. These spaces are significant as, among other uses, they form the building blocks of the infinite loop space construction QX^ [23], and are fundamental to certain constructions of Dyer-Lashof and Steenrod power operations; see, for example, [3].

[1]  Mark Hovey,et al.  Invertible Spectra in the E(n)‐Local Stable Homotopy Category , 1999 .

[2]  Mark Hovey,et al.  Morava K-theories and localisation , 1999 .

[3]  D. Ravenel,et al.  Brown–Peterson Cohomology from Morava K ‐Theory, II , 1998 .

[4]  I. Leary.  On the Integral Cohomology of Wreath Products , 1997, 0711.5017.

[5]  Michael A. Mandell,et al.  CHAPTER 6 – Modern Foundations for Stable Homotopy Theory , 1995 .

[6]  M. Hopkins,et al.  On the structure of spaces representing a landweber exact cohomology theory , 1995 .

[7]  Mark Hovey.  Bousfield Localization Functors and Hopkins' Chromatic Splitting Conjecture , 1993 .

[8]  A. Baker,et al.  Bockstein Operations in Morava K-Theories , 1991 .

[9]  Jon P. May,et al.  Equivariant Stable Homotopy Theory , 1986 .

[10]  J. McClure,et al.  H Ring Spectra and Their Applications , 1986 .

[11]  J. McClure,et al.  On the K-theory of the extended power construction , 1982, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  N. Yagita.  On the Steenrod algebra of Morava K-theory , 1980 .

[13]  D. Ravenel,et al.  THE MORAVA K-THEORIES OF EILENBERG-MACLANE SPACES AND THE CONNER-FLOYD CONJECTURE , 1980 .

[14]  U. Würgler.  On products in a family of cohomology theories associated to the invariant prime ideals of π*(BP)(BP) , 1977 .

[15]  P. Landweber.  Homological Properties of Comodules Over MU ∗ (MU) and BP ∗ (BP) , 1976 .

[16]  D. Ravenel,et al.  The Hopf ring for complex cobordism , 1974 .

[17]  V. Snaith.  A Stable Decomposition of ωNSnX , 1974 .

[18]  D. Lazard.  Autour de la platitude , 1969 .

[19]  M. Nakaoka.  HOMOLOGY OF THE INFINITE SYMMETRIC GROUP , 1961 .

[20]  J. Milnor.  THE STEENROD ALGEBRA AND ITS DUAL1 , 1958 .