The Borel and genuine $C_2$-equivariant Adams spectral sequences

TL;DR

This paper explores the relationships between classical, Borel, and genuine $C_2$-equivariant Adams spectral sequences, providing insights into their computations and connections for 2-completed spheres.

Contribution

It establishes a link between the Borel and genuine $C_2$-equivariant Adams spectral sequences, enabling their understanding and computation through classical Adams spectral sequences.

Findings

Relations between classical and equivariant spectral sequences are identified.

The Borel Adams spectral sequence is shown to be computable as a classical spectral sequence.

Insights into the structure of the genuine $C_2$-equivariant Adams spectral sequence are provided.

Abstract

We find out some relations between the classical Adams spectral sequences for stunted real projective spectra, the Borel $C_2$-equivariant Adams spectral sequence for the 2-completed sphere, and the genuine $C_2$-equivariant Adams spectral sequence for the 2-completed sphere. This allows us to understand the genuine $C_2$-equivariant Adams spectral sequence from the Borel Adams spectral sequences. We show that the Borel Adams spectral sequence is computable as a classical Adams spectral sequence.