000			03016cam a22003138i 4500
001			135874
003			ISI Library, Kolkata
005			20150616112231.0
008			140723s2014 riu b 000 0 eng
020			_a9781470418847 (alk. paper)
040			_aISI Library
082			_a510MS _223 _bAm512
245	1	0	_aTopological modular forms / _c[edited by] Christopher L. Douglas...[et al.].
260			_aProvidence : _bAmerican Mathematical Society, _cc2014.
300			_axxxi, 318 p. : _billustrations ; _c26 cm.
490	0		_aMathematical surveys and monographs ; _vv 201.
504			_aIncludes bibliographical references.
505	0		_aPart I 1. Elliptic genera and elliptic cohomology by C. Redden-- 2. Ellliptic curves and modular forms by C. Mautner-- 3. The moduli stack of elliptic curves by A. Henriques-- 4. The Landweber exact functor theorem by H. Hohnhold-- 5. Sheaves in homotopy theory by C. L. Douglas-- 6. Bousfield localization and the Hasse square by T. Bauer-- 7. The local structure of the moduli stack of formal groups by J. Lurie-- 8. Goerss-Hopkins obstruction theory by V. Angeltveit-- 9. From spectra to stacks by M. Hopkins-- 10. The string orientation by M. Hopkins-- 11. The sheaf of E ring spectra by M. Hopkins-- 12. The construction of tmf by M. Behrens-- 13. The homotopy groups of tmf and of its localizations by A. Henriques-- Part II 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 K(1)-local E ring spectra by M. J. Hopkins-- Glossary.
520			_aThis 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.
650		0	_aTopological fields.
650		0	_aAlgebraic fields.
650		0	_aElliptic Curves.
650		7	_aAlgebraic topology -- Homology and cohomology theories -- Elliptic cohomology.
700	1		_aDouglas, Christopher L., _eeditor
700	1		_aFrancis, John, _eeditor
700	1		_aHenriques, Andre G., _eeditor
700	1		_aHill, Michael A., _eeditor
942			_2ddc _cBK
999			_c419035 _d419035