1111.4520 (Carl McTague)

The Cayley plane and String bordism    [PDF]

Carl McTague

This paper shows that the kernel of the Witten genus tensor Z[1/6] is generated by total spaces of Cayley plane bundles, 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. This paper also shows that tmf is not a ring spectrum quotient of string bordism.

View original: http://arxiv.org/abs/1111.4520