Stable Homotopy Around The Arf Kervaire Invariant

Author : Victor P. Snaith
Publisher : Birkhäuser
Page : 239 pages
File Size : 52,5 Mb
Release : 2009-08-29
Category : Mathematics
ISBN : 3764399341

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Stable Homotopy Around the Arf-Kervaire Invariant by Victor P. Snaith Pdf

Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .

Author : Victor P. Snaith
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 55,6 Mb
Release : 2009-03-28
Category : Mathematics
ISBN : 9783764399047

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Stable Homotopy Around the Arf-Kervaire Invariant by Victor P. Snaith Pdf

Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .

Author : Michael A. Hill,Michael J. Hopkins,Douglas C. Ravenel
Publisher : Cambridge University Press
Page : 881 pages
File Size : 48,5 Mb
Release : 2021-07-29
Category : Mathematics
ISBN : 9781108831444

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Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by Michael A. Hill,Michael J. Hopkins,Douglas C. Ravenel Pdf

A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.

Author : Stanley O. Kochman
Publisher : Springer
Page : 338 pages
File Size : 43,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540469933

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Stable Homotopy Groups of Spheres by Stanley O. Kochman Pdf

A central problem in algebraic topology is the calculation of the values of the stable homotopy groups of spheres +*S. In this book, a new method for this is developed based upon the analysis of the Atiyah-Hirzebruch spectral sequence. After the tools for this analysis are developed, these methods are applied to compute inductively the first 64 stable stems, a substantial improvement over the previously known 45. Much of this computation is algorithmic and is done by computer. As an application, an element of degree 62 of Kervaire invariant one is shown to have order two. This book will be useful to algebraic topologists and graduate students with a knowledge of basic homotopy theory and Brown-Peterson homology; for its methods, as a reference on the structure of the first 64 stable stems and for the tables depicting the behavior of the Atiyah-Hirzebruch and classical Adams spectral sequences through degree 64.

Author : Rob de Jeu,James Dominic Lewis
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 55,5 Mb
Release : 2009
Category : Algebraic cycles
ISBN : 9780821844946

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Motives and Algebraic Cycles by Rob de Jeu,James Dominic Lewis Pdf

Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic $K$-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.

Author : Kishore Marathe
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 44,7 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9781848829398

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Topics in Physical Mathematics by Kishore Marathe Pdf

As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory. Other areas to emerge in this area are those derived from the works of Donaldson, Chern-Simons, Floer-Fukaya, and Seiberg-Witten. Aimed at a wide audience, Physical Topics in Mathematics demonstrates how various physical theories have played a crucial role in the developments of Mathematics and in particular, Geometric Topology. Issues are studied in great detail, and the book steadfastly covers the background of both Mathematics and Theoretical Physics in an effort to bring the reader to a deeper understanding of their interaction. Whilst the world of Theoretical Physics and Mathematics is boundless; it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader through the world of Physical Mathematics; leaving them with a choice of which realm they wish to visit next.

Author : Moti Mizrahi
Publisher : Rowman & Littlefield
Page : 224 pages
File Size : 48,5 Mb
Release : 2017-12-06
Category : Philosophy
ISBN : 9781786603425

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The Kuhnian Image of Science by Moti Mizrahi Pdf

More than 50 years after the publication of Thomas Kuhn’s seminal book, The Structure of Scientific Revolutions, this volume assesses the adequacy of the Kuhnian model in explaining certain aspects of science, particularly the social and epistemic aspects of science. One argument put forward is that there are no good reasons to accept Kunh’s incommensurability thesis, according to which scientific revolutions involve the replacement of theories with conceptually incompatible ones. Perhaps, therefore, it is time for another “decisive transformation in the image of science by which we are now possessed.” Only this time, the image of science that needs to be transformed is the Kuhnian one. Does the Kuhnian image of science provide an adequate model of scientific practice? If we abandon the Kuhnian picture of revolutionary change and incommensurability, what consequences would follow from that vis-à-vis our understanding of scientific knowledge as a social endeavour? The essays in this collection continue this debate, offering a critical examination of the arguments for and against the Kuhnian image of science as well as their implications for our understanding of science as a social and epistemic enterprise.

Author : Douglas C. Ravenel
Publisher : American Mathematical Society
Page : 417 pages
File Size : 44,7 Mb
Release : 2023-02-09
Category : Mathematics
ISBN : 9781470472931

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Complex Cobordism and Stable Homotopy Groups of Spheres by Douglas C. Ravenel Pdf

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 : Samuel Gitler,José Adem
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 43,6 Mb
Release : 1982
Category : Mathematics
ISBN : 9780821850107

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Symposium on Algebraic Topology in Honor of Jose Adem by Samuel Gitler,José Adem Pdf

Author : William Browder
Publisher : Unknown
Page : 108 pages
File Size : 43,9 Mb
Release : 1967
Category : Algebraic topology
ISBN : STANFORD:36105016304300

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The Kervaire Invariant of Framed Manifolds and Its Generalization by William Browder Pdf

Author : James Carlson
Publisher : American Mathematical Soc.
Page : 185 pages
File Size : 44,9 Mb
Release : 2014-10-16
Category : Mathematics
ISBN : 9780821898659

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The Poincare Conjecture by James Carlson Pdf

The conference to celebrate the resolution of the Poincare conjecture, which is one of the Clay Mathematics Institute's seven Millennium Prize Problems, was held at the Institut Henri Poincare in Paris. Several leading mathematicians gave lectures providing an overview of the conjecture--its history, its influence on the development of mathematics, and, finally, its proof. This volume contains papers based on the lectures at that conference. Taken together, they form an extraordinary record of the work that went into the solution of one of the great problems of mathematics.

Author : Arthur James Wells
Publisher : Unknown
Page : 1922 pages
File Size : 44,7 Mb
Release : 2009
Category : Bibliography, National
ISBN : STANFORD:36105211722678

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The British National Bibliography by Arthur James Wells Pdf

Author : R. James Milgram
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 41,5 Mb
Release : 1978
Category : Mathematics
ISBN : 9780821814321

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Algebraic and Geometric Topology by R. James Milgram Pdf

Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.

Author : Eric Peterson
Publisher : Cambridge University Press
Page : 421 pages
File Size : 52,5 Mb
Release : 2019
Category : Mathematics
ISBN : 9781108428033

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Formal Geometry and Bordism Operations by Eric Peterson Pdf

Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 50,7 Mb
Release : 2019-08-23
Category : Algebraic topology
ISBN : 9781470452063

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Lectures on Field Theory and Topology by Daniel S. Freed Pdf

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.