Article contents
Obstruction theory and the level n elliptic genus
Published online by Cambridge University Press: 03 August 2023
Abstract
Given a height at most two 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
$n\, {\geq}\, 2$.
- Type
- Research Article
- Information
- Copyright
- © 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
Footnotes
During the course of this work, the author was supported by NSF Grants DGE-1745302 and DMS-2103236.
References
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