New York Journal of Mathematics
Volume 27 (2021), 1134-1172


Hadi Zare

The Dyer-Lashof algebra and the hit problems

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Published: August 7, 2021.
Keywords: Dyer-Lashof algebra, Becker-Gottlieb transfer, infinite loop space.
Subject: 55S10, 55S12, 55P47.

We use work of Curtis and Wellington on A-annihilated classes in H*QS0 together with Priddy's computations on the action of the Dyer-Lashof algebra on
H*(Z x BO) to provide new examples of A-annihilated classes in H*BO as well H*BO(2r-1). We then consider the Becker-Gottlieb transfer associated to O(1)xn → O(n) and speculate on the possible applications of our computations to obtain new examples of A-annihilated classes in H*BO(1)n. Our results, all at the prime p=2, provide new numerical conditions which seem to show up for the first time in this context.


This work is partially supported by a grant from the Iranian National Science Foundation (INSF) Grant No. 98023105.

Author information

Hadi Zare:
School of Mathematics, Statistics, and Computer Science
College of Science
University of Tehran
Tehran 14174, Iran