Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Higher structure in the unstable Adams spectral sequence

Pages: 69 – 94

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a5


Samik Basu (Stat-Math Unit, Indian Statistical Institute, Kolkata, India)

David Blanc (Department of Mathematics, University of Haifa, Israel)

Debasis Sen (Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India)


We describe a variant construction of the unstable Adams spectral sequence for a space $\mathbf{Y}$, associated to any free simplicial resolution of $H^{\ast} (\mathbf{Y} ; R)$, for $R = \mathbb{F}_p$ or $\mathbb{Q}$. We use this construction to describe the differentials and filtration in the spectral sequence in terms of appropriate systems of higher cohomology operations.


unstable Adams spectral sequence, higher cohomology operations, differentials, cosimplicial resolutions

2010 Mathematics Subject Classification

Primary 55T15. Secondary 55P60, 55S20.

Received 2 June 2020

Received revised 11 October 2020

Accepted 12 October 2020

Published 7 April 2021