The Cayley plane and String bordism
Algebraic Topology
2014-11-11 v5 Mathematical Physics
Algebraic Geometry
Differential Geometry
math.MP
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 >3.
Cite
@article{arxiv.1111.4520,
title = {The Cayley plane and String bordism},
author = {Carl McTague},
journal= {arXiv preprint arXiv:1111.4520},
year = {2014}
}
Comments
27 pages, significantly improved exposition following suggestions by Haynes Miller