Real motivic and $C_2$-equivariant Mahowald invariants
| Autor: | Quigley, J. D. |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/topo.12185 |
| Popis: | We generalize the Mahowald invariant to the $\mathbb{R}$-motivic and $C_2$-equivariant settings. For all $i>0$ with $i \equiv 2,3 \mod 4$, we show that the $\mathbb{R}$-motivic Mahowald invariant of $(2+\rho \eta)^i \in \pi_{0,0}^{\mathbb{R}}(S^{0,0})$ contains a lift of a certain element in Adams' classical $v_1$-periodic families, and for all $i > 0$, we show that the $\mathbb{R}$-motivic Mahowald invariant of $\eta^i \in \pi_{i,i}^{\mathbb{R}}(S^{0,0})$ contains a lift of a certain element in Andrews' $\mathbb{C}$-motivic $w_1$-periodic families. We prove analogous results about the $C_2$-equivariant Mahowald invariants of $(2+\rho \eta)^i \in \pi_{0,0}^{C_2}(S^{0,0})$ and $\eta^i \in \pi_{i,i}^{C_2}(S^{0,0})$ 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 $\mathbb{R}$-motivic and $C_2$-equivariant settings. Comment: v2: 45 pages, substantially revised from v1. To appear in the Journal of Topology |
| Databáze: | arXiv |
| Externí odkaz: |
|