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Real motivic and C2‐equivariant Mahowald invariants
Journal of Topology  (IF1.582),  Pub Date : 2021-03-18, DOI: 10.1112/topo.12185
J.D. Quigley

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.