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Overview"During the winter term 1987/88 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 genus 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 equals 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 genera 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 manifold." Full Product DetailsAuthor: Friedrich Hirzebruch , Thomas Berger , Rainer Jung , Peter LandweberPublisher: Springer Fachmedien Wiesbaden Imprint: Vieweg+Teubner Verlag Edition: 1992 ed. Volume: E 20 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 0.355kg ISBN: 9783528064143ISBN 10: 3528064145 Pages: 212 Publication Date: 01 January 1992 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In stock We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Language: German Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |