# The cohomology of the Steenrod algebra and the mod $p$ Lannes-Zarati homomorphism

## TL;DR

This paper computes low-degree Ext groups over the Steenrod algebra and explores the properties of the Lannes-Zarati homomorphism for odd primes, advancing understanding of algebraic topology structures.

## Contribution

It provides explicit calculations of Ext groups for the Steenrod algebra at low degrees and analyzes the behavior of the Lannes-Zarati homomorphism for odd primes.

## Key findings

- Computed Ext groups for s ≤ 1 over the Steenrod algebra.
- Analyzed the behavior of the Lannes-Zarati homomorphism at low degrees.
- Enhanced understanding of algebraic structures in stable homotopy theory.

## Abstract

In this paper, we compute ${\rm Ext}_{A}^{s}(\widetilde{H}^*(B\mathbb{Z}/p),\mathbb{F}_p)$ for $s\leq 1$. Using this result, we investigate the behavior of $\varphi_3^{\mathbb{F}_p}$ and $\varphi_s^{\widetilde{H}^*(B\mathbb{Z}/p)}\ (s\leq1)$ for an odd prime $p$.

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Source: https://tomesphere.com/paper/1905.00819