Share

A Course on Surgery Theory

2021-01-26 MATHEMATICS
Download A Course on Surgery Theory PDF Online Free

Author :
Release : 2021-01-26
Genre : MATHEMATICS
Kind : eBook
Book Rating : 49X/5 ( reviews)

GET EBOOK


Book Synopsis A Course on Surgery Theory by : Stanley Chang

Download or read book A Course on Surgery Theory written by Stanley Chang. This book was released on 2021-01-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Surgery Theory

2024 Surgery (Topology)
Download Surgery Theory PDF Online Free

Author :
Release : 2024
Genre : Surgery (Topology)
Kind : eBook
Book Rating : 344/5 ( reviews)

GET EBOOK


Book Synopsis Surgery Theory by : Wolfgang Lück

Download or read book Surgery Theory written by Wolfgang Lück. This book was released on 2024. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.

Surgery on Compact Manifolds

1999 Mathematics
Download Surgery on Compact Manifolds PDF Online Free

Author :
Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 423/5 ( reviews)

GET EBOOK


Book Synopsis Surgery on Compact Manifolds by : Charles Terence Clegg Wall

Download or read book Surgery on Compact Manifolds written by Charles Terence Clegg Wall. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic and Geometric Surgery

2002 Mathematics
Download Algebraic and Geometric Surgery PDF Online Free

Author :
Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 240/5 ( reviews)

GET EBOOK


Book Synopsis Algebraic and Geometric Surgery by : Andrew Ranicki

Download or read book Algebraic and Geometric Surgery written by Andrew Ranicki. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in Simple-Homotopy Theory

2012-12-06 Mathematics
Download A Course in Simple-Homotopy Theory PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 728/5 ( reviews)

GET EBOOK


Book Synopsis A Course in Simple-Homotopy Theory by : M.M. Cohen

Download or read book A Course in Simple-Homotopy Theory written by M.M. Cohen. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geo metrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built. This belief is buttressed by the fact that the major uses of, and advances in, the theory in recent times-for example, the s-cobordism theorem (discussed in §25), the use of the theory in surgery, its extension to non-compact complexes (discussed at the end of §6) and the proof of topological invariance (given in the Appendix)-have come from just such an understanding. A second reason for writing the book is pedagogical. This is an excellent subject for a topology student to "grow up" on. The interplay between geometry and algebra in topology, each enriching the other, is beautifully illustrated in simple-homotopy theory. The subject is accessible (as in the courses mentioned at the outset) to students who have had a good one semester course in algebraic topology. I have tried to write proofs which meet the needs of such students. (When a proof was omitted and left as an exercise, it was done with the welfare of the student in mind. He should do such exercises zealously.

You may also like...