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Author: Daniel C. Isaksen
Publisher: American Mathematical Soc.
ISBN: 1470437880
Category : Education
Languages : en
Pages : 159
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Book Description
The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, the author also resolves all hidden extensions by 2, η, and ν through the 59-stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences. The author also computes the motivic stable homotopy groups of the cofiber of the motivic element τ. This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of τ are the same as the E2-page of the classical Adams-Novikov spectral sequence. This allows him to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.
Author: Daniel C. Isaksen
Publisher: American Mathematical Soc.
ISBN: 1470437880
Category : Education
Languages : en
Pages : 159
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Book Description
The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, the author also resolves all hidden extensions by 2, η, and ν through the 59-stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences. The author also computes the motivic stable homotopy groups of the cofiber of the motivic element τ. This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of τ are the same as the E2-page of the classical Adams-Novikov spectral sequence. This allows him to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.
Author: Stanley O. Kochman
Publisher: American Mathematical Soc.
ISBN: 0821825585
Category : Mathematics
Languages : en
Pages : 105
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Book Description
This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.
Author: Douglas C. Ravenel
Publisher: American Mathematical Soc.
ISBN: 082182967X
Category : Mathematics
Languages : en
Pages : 418
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Book Description
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Author: Stanley O. Kochman
Publisher: American Mathematical Soc.
ISBN: 9780821806005
Category : Mathematics
Languages : en
Pages : 294
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Book Description
This book is a compilation of lecture notes that were prepared for the graduate course ``Adams Spectral Sequences and Stable Homotopy Theory'' given at The Fields Institute during the fall of 1995. The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems. Suitable as a text for an intermediate course in algebraic topology, this book provides a direct exposition of the basic concepts of bordism, characteristic classes, Adams spectral sequences, Brown-Peterson spectra and the computation of stable stems. The key ideas are presented in complete detail without becoming encyclopedic. The approach to characteristic classes and some of the methods for computing stable stems have not been published previously. All results are proved in complete detail. Only elementary facts from algebraic topology and homological algebra are assumed. Each chapter concludes with a guide for further study.
Author: John Stewart
Publisher:
ISBN:
Category : Horses
Languages : en
Pages : 396
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Book Description
Author: Esther Rivas Adrover
Publisher: Laurence King Publishing
ISBN: 1780677952
Category : Architecture
Languages : en
Pages : 204
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Book Description
Deployable structures can expand and contract due to their geometrical, material and mechanical properties – offering the potential to create truly transforming environments. This book looks at the cutting edge of the subject, examining the different types of deployable structures and numerous design approaches. Filled with photographs, models, drawings and diagrams, Deployable Structures is packed with inspirational ideas for architecture students and practitioners.
Author: Pierre Le Béguec
Publisher: Springer
ISBN: 3319036149
Category : Medical
Languages : en
Pages : 138
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Book Description
Choosing an uncemented femoral prosthesis means first choosing a concept and to be effective, an operator has to have access to all the information that will allow them to reach the desired goals. This is the first step to be made. The quality of a surgical procedure does not depend on the manual skills of the surgeon performing it, but on how he has prepared and performed the operation “virtually” before actually performing it. This is the second step. An operating technique must be adapted to the chosen concept and the purpose of every surgical procedure must be clearly formulated and understood by the operator. This is the third step. Every surgeon has to have a reliable and rigorous radiological method of analysis for evaluating overall results and which suggests ways of improving results.
Author: Fred Corry Bishopp
Publisher:
ISBN:
Category : Livestock
Languages : en
Pages : 40
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Book Description
Author: Urs Feller
Publisher: MDPI
ISBN: 3038970638
Category : Science
Languages : en
Pages : 173
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Book Description
(This book is a printed edition of the Special Issue "Plant Nutrient Dynamics in Stressful Environments" that was published in Agriculture
Author: Nomy Arpaly
Publisher: Oxford University Press
ISBN: 0199882320
Category : Philosophy
Languages : en
Pages : 214
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Book Description
Nomy Arpaly rejects the model of rationality used by most ethicists and action theorists. Both observation and psychology indicate that people act rationally without deliberation, and act irrationally with deliberation. By questioning the notion that our own minds are comprehensible to us--and therefore questioning much of the current work of action theorists and ethicists--Arpaly attempts to develop a more realistic conception of moral agency.
