The Witten genus is the genus associated to the characteristic power series
where σL is the Weierstrass sigma function for the lattice L, and G is a multiple of an Eisenstein series.
The Witten genus of a 4k dimensional compact oriented smooth spin manifold with vanishing first Pontryagin class is a modular form of weight 2k, with integral Fourier coefficients.
Read more about this topic: Genus Of A Multiplicative Sequence
Famous quotes containing the word genus:
“Methinks it would be some advantage to philosophy if men were named merely in the gross, as they are known. It would be necessary only to know the genus and perhaps the race or variety, to know the individual. We are not prepared to believe that every private soldier in a Roman army had a name of his own,—because we have not supposed that he had a character of his own.”
—Henry David Thoreau (1817–1862)