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arXiv · 1911.10534

The Ando-Hopkins-Rezk orientation is surjective

Sanath K. Devalapurkar
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Abstract

We show that the map $\pi_\ast \mathrm{MString}\to \pi_\ast \mathrm{tmf}$ induced by the Ando-Hopkins-Rezk orientation is surjective. This proves an unpublished claim of Hopkins and Mahowald. We do so by constructing an $\mathbf{E}_1$-ring $B$ and a map $B \to \mathrm{MString}$ such that the composite $B \to \mathrm{MString} \to \mathrm{tmf}$ is surjective on homotopy. Applications to differential topology, and in particular to Hirzebruch's prize question, are discussed.

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Sanath K. Devalapurkar. 2019-11-24. The Ando-Hopkins-Rezk orientation is surjective. https://arxiv.org/abs/1911.10534

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