The Geometric Hopf Invariant And Surgery Theory
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Author | : Michael Crabb |
Publisher | : Springer |
Total Pages | : 405 |
Release | : 2018-01-24 |
Genre | : Mathematics |
ISBN | : 331971306X |
Download The Geometric Hopf Invariant and Surgery Theory Book in PDF, Epub and Kindle
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new.
Author | : Andrew Ranicki |
Publisher | : Oxford University Press |
Total Pages | : 386 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0198509243 |
Download Algebraic and Geometric Surgery Book in PDF, Epub and Kindle
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.
Author | : Tammo tom Dieck |
Publisher | : Birkhauser |
Total Pages | : 132 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : |
Download Surgery Theory and Geometry of Representations Book in PDF, Epub and Kindle
Author | : Andrew Ranicki |
Publisher | : Clarendon Press |
Total Pages | : 386 |
Release | : 2002-09-26 |
Genre | : Mathematics |
ISBN | : 0191545244 |
Download Algebraic and Geometric Surgery Book in PDF, Epub and Kindle
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.
Author | : Peter L. Duren |
Publisher | : American Mathematical Soc. |
Total Pages | : 602 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 9780821801307 |
Download A Century of Mathematics in America Book in PDF, Epub and Kindle
The first section of the book deals with some of the influential mathematics departments in the United States. Functioning as centers of research and training, these departments played a major role in shaping the mathematical life in this country. The second section deals with an extraordinary conference held at Princeton in 1946 to commemorate the university's bicentennial. The influence of women in American mathematics, the burgeoning of differential geometry in the last 50 years, and discussions of the work of von Karman and Weiner are among other topics covered.
Author | : Andrew Ranicki |
Publisher | : Oxford University Press |
Total Pages | : 396 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780198509240 |
Download Algebraic and Geometric Surgery Book in PDF, Epub and Kindle
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, co-bordism, 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.
Author | : David Mumford |
Publisher | : Springer Science & Business Media |
Total Pages | : 314 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9783540569633 |
Download Geometric Invariant Theory Book in PDF, Epub and Kindle
"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.
Author | : Karl H. Dovermann |
Publisher | : Springer |
Total Pages | : 234 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540463941 |
Download Equivariant Surgery Theories and Their Periodicity Properties Book in PDF, Epub and Kindle
The theory of surgery on manifolds has been generalized to categories of manifolds with group actions in several different ways. This book discusses some basic properties that such theories have in common. Special emphasis is placed on analogs of the fourfold periodicity theorems in ordinary surgery and the roles of standard general position hypotheses on the strata of manifolds with group actions. The contents of the book presuppose some familiarity with the basic ideas of surgery theory and transformation groups, but no previous knowledge of equivariant surgery is assumed. The book is designed to serve either as an introduction to equivariant surgery theory for advanced graduate students and researchers in related areas, or as an account of the authors' previously unpublished work on periodicity for specialists in surgery theory or transformation groups.
Author | : Charles Terence Clegg Wall |
Publisher | : American Mathematical Soc. |
Total Pages | : 321 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821809423 |
Download Surgery on Compact Manifolds Book in PDF, Epub and Kindle
The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
Author | : Stanley Chang |
Publisher | : Princeton University Press |
Total Pages | : 442 |
Release | : 2021-01-26 |
Genre | : MATHEMATICS |
ISBN | : 069116049X |
Download A Course on Surgery Theory Book in PDF, Epub and Kindle
An advanced treatment of surgery theory for graduate students and researchers Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest. Of significant use to high-dimensional topologists and researchers in noncommutative geometry and algebraic K-theory, A Course on Surgery Theory serves as an important resource for the mathematics community.