En genera

Chadwick, Steven Greg; Mandell, Michael A

doi:10.2140/gt.2015.19.3193

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$E_n$ genera

Steven Greg Chadwick and Michael A Mandell

Geometry & Topology 19 (2015) 3193–3232

DOI: 10.2140/gt.2015.19.3193

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 $π_{0} R$ , then every map of ring spectra $MSO \to R$ is represented by a map of $E_{2}$ ring spectra.

Keywords

genus, complex cobordism, oriented cobordism, $E_n$ ring spectrum, Thom spectrum, operadic algebra

Mathematical Subject Classification 2010

Primary: 55N22

Secondary: 55P43

References

Publication

Received: 18 November 2013

Revised: 3 March 2015

Accepted: 10 April 2015

Published: 6 January 2016

Proposed: Mark Behrens

Seconded: Ralph Cohen, Bill Dwyer

Authors

Steven Greg Chadwick
Department of Mathematics University of Maryland 4176 Campus Drive – Mathematics Building College Park, MD 20742-4015 USA

Michael A Mandell
Department of Mathematics Indiana University Rawles Hall 831 E 3rd St Bloomington, IN 47405 USA

Volume 19, issue 6 (2015)