Read & Download Manifolds and Modular Forms Aspects of Mathematics
Era depend on a parameter For special values of the parameter one obtains the signature and the A genus Indeed the universal elliptic genus can be regarded as a modular form with respect to the subgroup r 2 of the modular group; the two cusps o giving the signature and the A genus Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifol.
review à PDF, DOC, TXT or eBook Ô Friedrich Hirzebruch
During the winter term 198788 I gave a course at the University of Bonn under the title Manifolds and Modular Forms Iwanted to develop the theory of Elliptic Genera and to leam it myself on this occasion This theory due to Ochanine Landweber Stong and others was relatively new at the time The word genus is meant in the sense of my book Neue Topologische Methoden in der Algebraischen Geometrie published in 1956 A g.
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Enus is a homomorphism of the Thom cobordism ring of oriented compact manifolds into the complex numbers Fundamental examples are the signature and the A genus The A genus euals the arithmetic genus of an algebraic manifold provided the first Chem class of the manifold vanishes According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure The elliptic gen.