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The total Steenrod operation is induced by an A∞ ring homomorphism

Published online by Cambridge University Press:  24 October 2008

A. Kozlowski
A. Kozlowski
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.
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Let X be a (based) space of the homotopy type of a CW-complex. Let H(X) denote the classical (ungraded) cohomology ring Πi≥0Hi (X;Z/2). In [1] Atiyah and Hirzebruch described the group of natural ring automorphisms of H(X) (‘cohomology automorphisms’) with group operation given by composition. They showed that is isomorphic to the group of formal power series of the form with group operation given by ‘substitution’ of one power series into another. In particular the most famous ‘cohomology automorphism’, the total Steenrod Square, corresponds to x + x2.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 3 , May 1987 , pp. 469 - 476
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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