#### Volume 19, issue 6 (2015)

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$E_n$ genera

### Steven Greg Chadwick and Michael A Mandell

Geometry & Topology 19 (2015) 3193–3232
##### Abstract

Let $R$ be an ${E}_{2}$ ring spectrum with zero odd-dimensional homotopy groups. Every map of ring spectra $MU\to R$ is represented by a map of ${E}_{2}$ ring spectra. If $2$ is invertible in ${\pi }_{0}R$, then every map of ring spectra $MSO\to R$ is represented by a map of ${E}_{2}$ ring spectra.

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##### Keywords
genus, complex cobordism, oriented cobordism, $E_n$ ring spectrum, Thom spectrum, operadic algebra
Primary: 55N22
Secondary: 55P43