Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the cohomology of stable two stage Postnikov systems


Author: John R. Harper
Journal: Trans. Amer. Math. Soc. 152 (1970), 375-388
MSC: Primary 55.50
DOI: https://doi.org/10.1090/S0002-9947-1970-0268892-2
MathSciNet review: 0268892
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the cohomology of certain fibre spaces. The spaces are the total spaces of stable two stage Postnikov systems. We study their cohomology as Hopf algebras over the Steenrod algebra. The first theorem determines the cohomology as a Hopf algebra over the ground field, the algebra structure being known previously. The second theorem relates the action of the Steenrod algebra to the Hopf algebra structure and other available structures. The work is in the direction of explicit computations of these structures but is not quite complete with regard to the action of the Steenrod algebra. The ideas of Massey and Peterson [7], Mem. Amer. Math. Soc. No. 74, are used extensively, and $ \bmod 2$ cohomology is used throughout.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55.50

Retrieve articles in all journals with MSC: 55.50


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0268892-2
Keywords: Fibration, fibre space, Postnikov system, Hopf algebra, Steenrod algebra, stable $ k$-invariant, Massey-Peterson fundamental sequence
Article copyright: © Copyright 1970 American Mathematical Society