The Cayley plane and string bordism

McTague, Carl

doi:10.2140/gt.2014.18.2045

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The Cayley plane and string bordism

Carl McTague

Geometry & Topology 18 (2014) 2045–2078

DOI: 10.2140/gt.2014.18.2045

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

References

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

Volume 18, issue 4 (2014)