Document Type
Article
Abstract
The bordism ring MU∗(CP∞) is central to the theory of formal groups as applied by D. Quillen, J. F. Adams, and others recently to complex cobordism. In the present paper, rings E∗(CP∞) are considered, where E is an oriented ring spectrum, R=π∗(E), and pR=0 for a prime p. It is known that E∗(CP∞) is freely generated as an R-module by elements {βτ|r≧0}. The ring structure, however, is not known. It is shown that the elements {βpτ|r≧0} form a simple system of generators for E∗(CP∞) and that βpτp≡spτβpτ mod(β₁,⋯,βpτ-1) for an element s ∈ R (which corresponds to [CPp-1] when E=MUZp). This may lead to information concerning E∗(K(Z,n)).
Disciplines
Mathematics
Recommended Citation
C. Schochet, On the bordism ring of complex projective space, Proceedings of the American Mathematical Society 37(1) (1973), 267-270.
Comments
First published in the Proceedings of the American Mathematical Society 37(1) (1973, http://dx.doi.org/10.1090/S0002-9939-1973-0307222-2), published by the American Mathematical Society.