Real motivic and C2‐equivariant Mahowald invariants. Issue 2 (18th March 2021) - Quigley, J.D.
Abstract: We generalize the Mahowald invariant to the R ‐motivic and C 2 ‐equivariant settings. For all i > 0 with i ≡ 2, 3 mod 4, we show that the R ‐motivic Mahowald invariant of ( 2 + ρ η ) i ∈ π 0, 0 R ( S 0, 0 ) contains a lift of a certain element in Adams' classical v 1 ‐periodic families, and for all i > 0, we show that the R ‐motivic Mahowald invariant of η i ∈ π i, i R ( S 0, 0 ) contains a lift of a certain element in Andrews' C ‐motivic w 1 ‐periodic families. We prove analogous results about the C 2 ‐equivariant Mahowald invariants of ( 2 + ρ η ) i ∈ π 0, 0 C 2 ( S 0, 0 ) and η i ∈ π i, i C 2 ( S 0, 0 ) by leveraging connections between the classical, motivic, and equivariant stable homotopy categories. The infinite families we construct are some of the first periodic families of their kind studied in the R ‐motivic and C 2 ‐equivariant settings.