Manifolds and Modular Forms (Aspects of Mathematics): Ed. by Max-Planck-Institut f. Mathematik Bonn (Aspects of Mathematics, 20, Band 20) - Softcover

Hirzebruch, F.

Softcover

ISBN 10: 352816414X ISBN 13: 9783528164140

Verlag: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1994

Inhaltsangabe

During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn 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 Thorn 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 Chern 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 0 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.

Über diesen Titel

Über die Autorin bzw. den Autor

Biography of Friedrich Hirzebruch Friedrich Hirzebruch was born on October 17, 1927 in Hamm, Germany. He studied mathematics at the University of Münster and the ETH Zürich, under Heinrich Behnke and Heinz Hopf. Shortly after the award of his doctoral degree in 1950, he obtained an assistantship in Erlangen and then a membership at the Institute for Advanced Study, Princeton, followed by an assistant professorship at Princeton University. In 1956 he returned to Germany to a chair at the University of Bonn, which he held until his retirement in 1993. Since 1980 he has been the Director of the Max Planck Institute for Mathematics in Bonn. Hirzebruch's work has been fundamental in combining topology, algebraic and differential geometry and number theory. It has had a deep and far-reaching influence on the work of many others, who have expanded and generalized his ideas. His most famous result is the theorem of Riemann-Roch-Hirzebruch.

Details zur Ausgabe

• Verlag: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
• Erscheinungsdatum: 1994
• Sprache: Englisch
• ISBN 10: 352816414X
• ISBN 13: 9783528164140
• Einband: Taschenbuch
• Auflage: 2
• Anzahl der Seiten: 228
• Kontakt zum Hersteller: Springer-Verlag GmbH; customerservice@springernature.com; ; Tiergartenstraße 17; Heidelberg; Baden-Württemberg; 69121; Deutschland