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OverviewThe theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss--Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald. Full Product DetailsAuthor: Christopher L. Douglas , John Francis , Andre G. Henriques , Michael A. HillPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 201 Weight: 0.778kg ISBN: 9781470418847ISBN 10: 1470418843 Pages: 315 Publication Date: 30 December 2014 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsElliptic genera and elliptic cohomology by C. Redden Ellliptic curves and modular forms by C. Mautner The moduli stack of elliptic curves by A. Henriques The Landweber exact functor theorem by H. Hohnhold Sheaves in homotopy theory by C. L. Douglas Bousfield localization and the Hasse square by T. Bauer The local structure of the moduli stack of formal groups by J. Lurie Goerss-Hopkins obstruction theory by V. Angeltveit From spectra to stacks by M. Hopkins The string orientation by M. Hopkins The sheaf of E ring spectra by M. Hopkins The construction of tmf by M. Behrens The homotopy groups of tmf and of its localizations by A. Henriques Ellitpic curves and stable homotopy I by M. J. Hopkins and H. R. Miller From elliptic curves to homotopy theory by M. Hopkins and M. Mahowald 1 E ring spectra by M. J. Hopkins Glossary by C. L. Douglas, J. Francis, A. G. Henriques, and M. A. HillReviewsAuthor InformationChristopher L. Douglas, Oxford University, United Kingdom. John Francis, Northwestern University, Evanston, IL, USA. Andre G. Henriques, Utrecht University, Netherlands. Michael A. Hill, University of Virginia, Charlottesville, VA, USA. Tab Content 6Author Website:Countries AvailableAll regions |
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