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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.