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Inspired by earlier work exhibiting ?1-periodicity in the topological cyclic homology of the integers, and subsequent work exhibiting ?2-periodicity in the topological cyclic homology of the connective complex K-theory ring spectrum and its Adams summand, Bruner and Rognes began investigating the topological Hochschild homology and topological cyclic homology of the topological modular forms ring spectrum, aiming to study the ?3-action on F*TC(tmf) for suitable type-three spectra F. They show that the Adams spectral sequence, in conjunction with the "ext" computer software package, provides a flexible and powerful tool for making calculations with tmf, THH(tmf) and approximations to TC(tmf). Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
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The Adams Spectral Sequence for Topological Modular Forms (Mathematical Surveys and Monographs) ; 253
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American Mathematical Society, 2021
ISBN 10: 1470456745
ISBN 13: 9781470456740
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Hardcover. Condizione: Very Good. As new, in original plastic wrapping, slightly torn. Book unopened.; 26.1 cms x 18.3 cms x 4.4 cms; 690 pages. Codice articolo LCB86059
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The Adams Spectral Sequence for Topological Modular Forms (Hardcover)
Editore:
American Mathematical Society, Providence, 2021
ISBN 10: 1470456745
ISBN 13: 9781470456740
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Hardcover. Condizione: new. Hardcover. 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 $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations. Gives 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9781470456740
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The Adams Spectral Sequence for Topological Modular Forms (Hardcover)
Editore:
American Mathematical Society, Providence, 2021
ISBN 10: 1470456745
ISBN 13: 9781470456740
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Hardcover. Condizione: new. Hardcover. 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 $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations. Gives 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9781470456740
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