New York Journal of Mathematics
Volume 30 (2024), 513-520


Donald M. Davis and W. Stephen Wilson

The cohomology of the connective spectra for K-theory revisited

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Published: March 31, 2024.
Keywords: Adem relations, connective K-theory, Steenrod algebra.
Subject [2020]: 55S10, 55R45, 55N15.

The stable mod 2 cohomologies of the spectra for connective real and complex K-theories are well known and easy to work with. However, the known bases are in terms of the anti-automorphism of Milnor basis elements. We offer simple bases in terms of admissible sequences of Steenrod operations that come from the Adem relations. In particular, a basis for H*(bu) is given by those SqI with I admissible and no Sq1 or Sq2n+1 appearing for n > 0.


We are grateful for the referee's very careful reading and many useful suggestions for improved exposition.

Author information

Donald M. Davis
Department of Mathematics
Lehigh University
Bethlehem, PA 18015, USA


W. Stephen Wilson
Department of Mathematics
Johns Hopkins University
Baltimore, MD 01220, USA