Surgery on Compact Manifolds

DOWNLOAD NOW »

Author: Charles Terence Clegg Wall,Andrew Ranicki,Department of Mathematics and Statistics Andrew Ranicki

Publisher: American Mathematical Soc.

ISBN: 0821809423

Category: Mathematics

Page: 302

View: 5885

A new edition of a classic book originally published in 1970 and now updated and expanded to include the very latest developments. The volume remains the single most important book on the topic. Features an attractive cover.

The Wild World of 4-manifolds

DOWNLOAD NOW »

Author: Alexandru Scorpan

Publisher: American Mathematical Soc.

ISBN: 0821837494

Category: Mathematics

Page: 609

View: 4098

What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. --MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.

Embeddings in Manifolds

DOWNLOAD NOW »

Author: Robert J. Daverman,Gerard Venema

Publisher: American Mathematical Soc.

ISBN: 0821836978

Category: Mathematics

Page: 468

View: 6868

A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.

Open Problems in Mathematics

DOWNLOAD NOW »

Author: John Forbes Nash, Jr.,Michael Th. Rassias

Publisher: Springer

ISBN: 3319321625

Category: Mathematics

Page: 543

View: 3661

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Automorphisms of Manifolds and Algebraic K-Theory: Part III

DOWNLOAD NOW »

Author: Michael S. Weiss, Bruce E. Williams

Publisher: American Mathematical Soc.

ISBN: 147040981X

Category: Mathematics

Page: 110

View: 4090

The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.

Surgery on Compact Manifolds

DOWNLOAD NOW »

Author: Charles Terence Clegg Wall,Andrew Ranicki,Department of Mathematics and Statistics Andrew Ranicki

Publisher: American Mathematical Soc.

ISBN: 0821809423

Category: Mathematics

Page: 302

View: 5034

A new edition of a classic book originally published in 1970 and now updated and expanded to include the very latest developments. The volume remains the single most important book on the topic. Features an attractive cover.

Surgery on Compact Manifolds

DOWNLOAD NOW »

Author: Charles Terence Clegg Wall,Andrew Ranicki,Department of Mathematics and Statistics Andrew Ranicki

Publisher: American Mathematical Soc.

ISBN: 0821809423

Category: Mathematics

Page: 302

View: 4267

A new edition of a classic book originally published in 1970 and now updated and expanded to include the very latest developments. The volume remains the single most important book on the topic. Features an attractive cover.

Geometry & Topology

DOWNLOAD NOW »

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: N.A

View: 1603

Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

Hilbert

DOWNLOAD NOW »

Author: Constance Reid,Hermann Weyl

Publisher: Springer-Verlag

ISBN: 3662286157

Category: Mathematics

Page: 290

View: 4955

Lehrbuch der Topologie

DOWNLOAD NOW »

Author: Herbert Seifert,William Threlfall

Publisher: University of Pennsylvania Press

ISBN: 9780821835951

Category: Mathematics

Page: 353

View: 3676

The 1930s were important years in the development of modern topology, pushed forward by the appearance of a few pivotal books, of which this is one. The focus is on combinatorial and algebraic topology, with as much point-set topology as needed for the main topics. One sees from the modern point of view that the authors are working in a category of spaces that includes locally finite simplicial complexes. (Their definition of manifold is more properly known today as a ""triangulizable homology manifold"".)Amazingly, they manage to accomplish a lot without the convenient tools of homological algebra, such as exact sequences and commutative diagrams, that were developed later. The main topics covered are: simplicial homology (coefficients in $\mathbb{Z}$ or $\mathbb{Z}_2$), local homology, surface topology, the fundamental group and covering spaces, three-manifolds, Poincare duality, and the Lefschetz fixed point theorem. Few prerequisites are necessary. A final section reviews the lemmas and theorems from group theory that are needed in the text. As stated in the introduction to the important book by Alexandroff and Hopf (which appeared a year after ""Seifert and Threlfall""): 'Its lively and instructive presentation makes this book particularly suitable as an introduction or as a textbook.'

BPR

DOWNLOAD NOW »

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4409

Vorstudien zur Topologie

DOWNLOAD NOW »

Author: Johann Benedikt Listing

Publisher: Рипол Классик

ISBN: N.A

Category: History

Page: 67

View: 1966

Poincarés Vermutung

die Geschichte eines mathematischen Abenteuers

DOWNLOAD NOW »

Author: Donal O'Shea

Publisher: N.A

ISBN: 9783596176632

Category:

Page: 376

View: 1404

Current Trends in Transformation Groups

DOWNLOAD NOW »

Author: Anthony Bak,Masaharu Morimoto,Fumihiro Ushitaki

Publisher: Springer Science & Business Media

ISBN: 9781402007835

Category: Mathematics

Page: 249

View: 1765

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.