Volume 18, issue 4 (2014)

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The Cayley plane and string bordism

Carl McTague

Geometry & Topology 18 (2014) 2045–2078
Abstract

This paper shows that, away from $6$, the kernel of the Witten genus is precisely the ideal consisting of (bordism classes of) Cayley plane bundles with connected structure group, but only after restricting the Witten genus to string bordism. It does so by showing that the divisibility properties of Cayley plane bundle characteristic numbers arising in Borel–Hirzebruch Lie group-theoretic calculations correspond precisely to the divisibility properties arising in the Hovey–Ravenel–Wilson $BP$ Hopf ring-theoretic calculation of string bordism at primes greater than $3$.

Keywords
Cayley plane, Witten genus, string bordism
Mathematical Subject Classification 2010
Primary: 57R90, 58J26
Publication
Received: 7 December 2011
Revised: 29 January 2014
Accepted: 27 February 2014
Published: 2 October 2014
Proposed: Haynes Miller
Seconded: Bill Dwyer, Ralph Cohen
Authors
 Carl McTague Mathematics Department Johns Hopkins University Baltimore, MD 21218 USA http://www.mctague.org/carl