Obstruction theory and the level $n$ elliptic genus

Andrew Senger

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arXiv · 2203.13743

Obstruction theory and the level $n$ elliptic genus

Andrew Senger

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Abstract

Given a height $\leq 2$ Landweber exact $\mathbb{E}_\infty$-ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the Ando criterion admits a unique lift to an $\mathbb{E}_\infty$-complex orientation $\mathrm{MU} \to E$. As a consequence, we give a short proof that the level $n$ elliptic genus lifts uniquely to an $\mathbb{E}_\infty$-complex orientation $\mathrm{MU} \to \mathrm{tmf}_1 (n)$ for all $n \geq 2$.

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Andrew Senger. 2022-03-25. Obstruction theory and the level $n$ elliptic genus. https://arxiv.org/abs/2203.13743

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