The cohomology of the projective -plane

Author:
William A. Thedford

Journal:
Proc. Amer. Math. Soc. **76** (1979), 327-332

MSC:
Primary 55R35; Secondary 57T25

MathSciNet review:
537099

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Abstract: An *H*-space is a topological space with a continuous multiplication and an identity element. In this paper *X* has the homotopy type of a countable CW-complex with integral cohomology of finite type and primitively generated *k*-cohomology, *k* a field. The projective *n*-plane 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 *k*-ideal, 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)*-sub-algebra 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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DOI:
https://doi.org/10.1090/S0002-9939-1979-0537099-7

Keywords:
*Z(p)*-cohomology of *H*-spaces,
Steenrod algebra,
projective plane of an *H*-space,
homotopy associativity

Article copyright:
© Copyright 1979
American Mathematical Society