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

Let R be an E2 ring spectrum with zero odd-dimensional homotopy groups. Every map of ring spectra MU R is represented by a map of E2 ring spectra. If 2 is invertible in π0R, then every map of ring spectra MSO R is represented by a map of E2 ring spectra.

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genus, complex cobordism, oriented cobordism, $E_n$ ring spectrum, Thom spectrum, operadic algebra
Mathematical Subject Classification 2010
Primary: 55N22
Secondary: 55P43
Received: 18 November 2013
Revised: 3 March 2015
Accepted: 10 April 2015
Published: 6 January 2016
Proposed: Mark Behrens
Seconded: Ralph Cohen, Bill Dwyer
Steven Greg Chadwick
Department of Mathematics
University of Maryland
4176 Campus Drive – Mathematics Building
College Park, MD 20742-4015
Michael A Mandell
Department of Mathematics
Indiana University
Rawles Hall
831 E 3rd St
Bloomington, IN 47405