论文标题
真实方向的奇数类似物
Odd primary analogs of Real orientations
论文作者
论文摘要
我们以$ c_p $ - equivariant同义理论定义$ p> 2 $，一个$μ_p$ - 方向的概念类似于$ c_2 $ equivariant的真实方向。该定义取决于$ C_P $ -SPACE $ \ MATHBB {cp}^{\ infty} _ {μ_p} $，即使在有意义地概括了最近的$ C_2 $ Equivariant在偶联空间上的工作，我们也证明了这一点。 我们证明，高度$ p-1 $ morava $ e $ - 理论为$μ_p$ - 面向和$ \ mathrm {tmf}（2）$是$μ_3$面向。我们解释了单个epivariant映射$ v_1^{μ_p}：s^{2ρ} \ toσ^{\ infty} \ Mathbb {cp}^{\ infty} _ {μ_p} $高度转移现象普遍存在，在含量的色度同义理论中。
We define, in $C_p$-equivariant homotopy theory for $p>2$, a notion of $μ_p$-orientation analogous to a $C_2$-equivariant Real orientation. The definition hinges on a $C_p$-space $\mathbb{CP}^{\infty}_{μ_p}$, which we prove to be homologically even in a sense generalizing recent $C_2$-equivariant work on conjugation spaces. We prove that the height $p-1$ Morava $E$-theory is $μ_p$-oriented and that $\mathrm{tmf}(2)$ is $μ_3$-oriented. We explain how a single equivariant map $v_1^{μ_p}:S^{2ρ} \to Σ^{\infty} \mathbb{CP}^{\infty}_{μ_p}$ completely generates the homotopy of $E_{p-1}$ and $\mathrm{tmf}(2)$, expressing a height-shifting phenomenon pervasive in equivariant chromatic homotopy theory.
