The Adams spectral sequence for topological modular forms /

The Adams spectral sequence for topological modular forms /

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Bibliographic Details
Author / Creator:	Bruner, R. R. (Robert Ray), 1950- author.
Imprint:	Providence, Rhode Island : American Mathematical Society, [2021] ©2021
Description:	xix, 690 pages : illustrations (some color) ; 26 cm.
Language:	English
Series:	Mathematical surveys and monographs, 0076-5376 ; Volume 253 Mathematical surveys and monographs ; no. 253.
Subject:	Algebra, Homological. Homology theory. Adams spectral sequences. Adams spectral sequences. Algebra, Homological. Homology theory.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12703697

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Other authors / contributors:	Rognes, John, author.
ISBN:	9781470456740 1470456745 9781470469580 1470469588 9781470465636
Notes:	Includes bibliographical references (pages 675-682) and index.
Summary:	"The connective topological modular forms spectrum, tmf, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of tmf and several tmf-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The H∞ ring structure of the sphere and of tmf are used to determine many differentials and relations."

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Call Number:	QA169.B765 2021 c.1
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