Formal Geometry And Bordism Operations
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Formal Geometry And Bordism Operations
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Author : Eric Peterson
language : en
Publisher: Cambridge University Press
Release Date : 2019
Formal Geometry And Bordism Operations written by Eric Peterson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.
Handbook Of Homotopy Theory
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Author : Haynes Miller
language : en
Publisher: CRC Press
Release Date : 2020-01-23
Handbook Of Homotopy Theory written by Haynes Miller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
Topology Geometry And Dynamics V A Rokhlin Memorial
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Author : Anatoly M. Vershik
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-30
Topology Geometry And Dynamics V A Rokhlin Memorial written by Anatoly M. Vershik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-30 with Education categories.
Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
Topological Library Part 1 Cobordisms And Their Applications
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Author : Serguei Petrovich Novikov
language : en
Publisher: World Scientific
Release Date : 2007-07-09
Topological Library Part 1 Cobordisms And Their Applications written by Serguei Petrovich Novikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-09 with Mathematics categories.
This is the first of three volumes collecting the original and now classic works in topology written in the 50s-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “Singular homologies of fibre spaces.”This is the translation of the Russian edition published in 2005 with one entry (Milnor's lectures on the h-cobordism) omitted.
Bordism Stable Homotopy And Adams Spectral Sequences
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Author : Stanley O. Kochman
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Bordism Stable Homotopy And Adams Spectral Sequences written by Stanley O. Kochman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Algebraic And Geometric Surgery
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Author : Andrew Ranicki
language : en
Publisher: Oxford University Press
Release Date : 2002
Algebraic And Geometric Surgery written by Andrew Ranicki and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
Formal Groups And Applications
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Author : Michiel Hazewinkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Formal Groups And Applications written by Michiel Hazewinkel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
Complex Cobordism And Stable Homotopy Groups Of Spheres
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Author : Douglas C. Ravenel
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-11-25
Complex Cobordism And Stable Homotopy Groups Of Spheres written by Douglas C. Ravenel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-25 with Mathematics categories.
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.
On Thom Spectra Orientability And Cobordism
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Author : Yu. B. Rudyak
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-12
On Thom Spectra Orientability And Cobordism written by Yu. B. Rudyak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-12 with Mathematics categories.
Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.
Lecture Notes In Algebraic Topology
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Author : James Frederic Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lecture Notes In Algebraic Topology written by James Frederic Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic andgeometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, someknowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstructiontheory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to presentproofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, andhomological algebra. The exposition in the text is clear; special cases are presented over complex general statements.