Real motivic and C2‐equivariant Mahowald invariants. Issue 2 (18th March 2021)

• Record Type: Journal Article
• Authors: Quigley, J.D.
• Is Part Of: Journal of topology. Volume 14:Issue 2(2021)
• Page Start: 369
• Page End: 418
• Publication Date: 2021-03-18
• Subjects: 14F42 -- 55P91 -- 55Q45 -- 55Q51 -- 55Q91 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12185
• Languages: English
• ISSNs: 1753-8416

Abstract

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.