THE ADAMS SPECTRAL SEQUENCE FOR U*(X, Zp) AND APPLICATIONS TO LIE GROUPS, ETC
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1. Preliminaries. In [ l ] the structure of the weakly complex bordism of 1 connected semisimple Lie groups was studied via the Milnor, Eilenberg-Moore, Rothenberg-Steenrod sequence. See [l] for notation. In this paper we amplify the Adams spectral sequence [2], [3], [4] and relate this tool to the weakly complex cobordism theory. The techniques apply to any finite CW complex. In particular we apply them to real projective spaces and to 1 connected compact semisimple Lie groups. As in the bordism theory [ l ] , it is useful to introduce coefficients into the cobordism theory. Zp coefficients arise via [5]. Let Ap U*(pt, Zp) = Zp[Yh F2, • • ] dim F< = 2f, * è 1 and define A p [ l /Fp_i] = direct lim 1/YP^XAP. Ap[l/Yp-.i] is the ring obtained from Ap by making Fp_i a unit. A p [ l /Fp_i] coefficients can be introduced. U*(X, Ap[l/Yp-i]) denotes the resulting theory. The techniques of this paper allow us to extend the theorems in [ l ] . For example:
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