The Adams spectral sequence for topological modular forms

by Bruner, R. R., (Robert Ray)

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Title Statements

Full title :The Adams spectral sequence for topological modular forms / Robert R. Bruner, John Rognes.

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."

Edition Statements

Publication Date:©2021

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2021

The Physical Object

Description:xix, 690 pages : : illustrations (some color) ; : 26 cm.

Edition Identifiers

ISBN:9781470456740, 1470456745, 9781470469580, 1470469588
oclc:on1242021766
LC Classification:QA169
Dewey Decimal:514/.23

Subjects

Adams spectral sequences Algebra, Homological Algebraic topology -- Homology and coho… Algebraic topology -- Homology and coho… Algebraic topology -- Homotopy groups -… Algebraic topology -- Homotopy groups -… Algebraic topology -- Homotopy theory -… Algebraic topology -- Homotopy theory -… Algebraic topology -- Spectral sequence… Algebraic topology -- Spectral sequence… ALGÈBRE HOMOLOGIQUE Category theory; homological algebra --… Homologie Homology theory Suites spectrales d'Adams