arXiv Open Access 2020

Odd primary analogs of Real orientations

Jeremy Hahn Andrew Senger Dylan Wilson

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Abstrak

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.

Topik & Kata Kunci

math.AT

Penulis (3)

Jeremy Hahn

Andrew Senger

Dylan Wilson

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APA MLA BibTeX

Hahn, J., Senger, A., Wilson, D. (2020). Odd primary analogs of Real orientations. https://arxiv.org/abs/2009.12716

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓