The algebraic Atiyah-Hirzebruch spectral sequence of real projective spectra

TL;DR

This paper computes the algebraic Atiyah-Hirzebruch spectral sequence for real projective spectra using Curtis's algorithm and Lambda algebra, providing detailed data on the Adams E2-page and transfer maps, aiding in homotopy group calculations.

Contribution

It introduces a computational approach to determine the algebraic Atiyah-Hirzebruch spectral sequence for real projective spectra, including transfer maps, with results extending the understanding of stable homotopy groups.

Findings

Computed Adams E2-page for $ ext{RP}^ $ in range t<72

Determined transfer map on Adams E2-pages

Provided data used in subsequent homotopy group calculations

Abstract

In this note, we use Curtis's algorithm and the Lambda algebra to compute the algebraic Atiyah-Hirzebruch spectral sequence of the suspension spectrum of $\mathbb{R}P^\infty$ with the aid of a computer, which gives us its Adams $E_2$-page in the range of $t<72$. We also compute the transfer map on the Adams $E_2$-pages. These data are used in our computations of the stable homotopy groups of $\mathbb{R}P^\infty$ in [6] and of the stable homotopy groups of spheres in [7].