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Carl McTague
mathematician, composer, photographer, fiddler |
The Cayley Plane and String Bordism
My new paper [published 2 Oct 2014]:
The Cayley Plane and String Bordism, Geometry & Topology 18-4 (2014), 2045–2078.
shows that an affinity between bordism rings and projective spaces extends further than previously known.
For those familiar with Milnor’s generators for the unoriented (respectively complex) bordism ring, namely degree-(1,1) hypersurfaces in products of projective spaces P^{m}×P^{n} over R (respectively C): I extend this construction to the String bordism ring MO⟨8⟩[1/6] using the Cayley Plane—the projective plane over the Octonions O. This involves showing that the arithmetic of Cayley plane bundle characteristic numbers arising in Borel–Hirzebruch Lie group-theoretic calculations correspond precisely to the arithmetic arising in the Hovey–Ravenel–Wilson BP Hopf ring-theoretic calculation of String bordism at primes greater than 3.