Topological Modular Forms (Hardcover)

The 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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Mathematical Surveys and Monographs
Release date:	December 2014
Editors:	Christopher L. Douglas • John Francis • Andre G. Henriques • Michael A. Hill
Dimensions:	254 x 178mm (L x W)
Format:	Hardcover
Pages:	315
ISBN-13:	978-1-4704-1884-7
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Geometry > General Books > Science & Mathematics > Mathematics > Topology > General Promotions
LSN:	1-4704-1884-3
Barcode:	9781470418847

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