The $C_2$-equivariant $K(1)$-local sphere

William, Balderrama,

doi:10.48550/arxiv.2103.13895

Cited by 1 publication

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. See for instance [Bal21] or [Bal22]; for the former note π s,w b(KO 2 ) = π s,s−w ν(KO) and η C2 = −η 0 , and for the latter note π s,w KO 2 = π (s−w)+wσ KO C2 ⊗Z 2 and η C2 = −η σ .…”

Section: Morava E-theorymentioning

confidence: 99%

“…( 21). This computation was also carried out in [Bal21], but our situation is much simpler: the hard work there was to pin down the ring structure on π * , * b(S K( 1) ), which we don't need, and even for the additive structure we need only the particular groups π 2n,n S K (1) . Because we need details of the computation, it is easier to just proceed directly.…”

Section: Morava E-theorymentioning

confidence: 99%

See 1 more Smart Citation

Total power operations in spectral sequences

William¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We describe how power operations descend through homotopy limit spectral sequences. We apply this to describe how norms appear in the C 2 -equivariant Adams spectral sequence, to compute norms on π 0 of the equivariant KU -local sphere, and to compute power operations for the K(1)-local sphere. An appendix contains material on equivariant Bousfield localizations that may be of independent interest. Contents 1. Introduction 2. Unstable naturality of the homotopy limit spectral sequence 3. Looping power operations 4. Norms in the C 2 -equivariant Adams spectral sequence 5. Norms on π 0 of the equivariant KU -local sphere 6. Power operations for the K(1)-local sphere Appendix A. Equivariant Bousfield localizations References

show abstract

Section: Morava E-theorymentioning

confidence: 99%

Section: Morava E-theorymentioning

confidence: 99%