The cohomology of the projective plane
Author:
William A. Thedford
Journal:
Proc. Amer. Math. Soc. 76 (1979), 327332
MSC:
Primary 55R35; Secondary 57T25
MathSciNet review:
537099
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Abstract: An Hspace is a topological space with a continuous multiplication and an identity element. In this paper X has the homotopy type of a countable CWcomplex with integral cohomology of finite type and primitively generated kcohomology, k a field. The projective nplane of X is denoted . The main results of this paper are: Theorem 1 which states that where N is a truncated polynomial algebra over k and S is a trivial kideal, and Theorem 2 which considers the case and states that where is a truncated polynomial algebra on generators in even dimensions and S is an A(p)subalgebra of so that an A(p)algebra structure can be induced on . These theorems extend results by A. Borel, W. Browder, M. Rothenberg, N. E. Steenrod, and E. Thomas.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905370997
PII:
S 00029939(1979)05370997
Keywords:
Z(p)cohomology of Hspaces,
Steenrod algebra,
projective plane of an Hspace,
homotopy associativity
Article copyright:
© Copyright 1979 American Mathematical Society
