## Surgery on Compact Manifolds

**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:**4310

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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

**Author**: Alexandru Scorpan

**Publisher:**American Mathematical Soc.

**ISBN:**0821837494

**Category:**Mathematics

**Page:**609

**View:**1799

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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

**Author**: Robert J. Daverman,Gerard Venema

**Publisher:**American Mathematical Soc.

**ISBN:**0821836978

**Category:**Mathematics

**Page:**468

**View:**7727

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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

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

**Publisher:**Springer

**ISBN:**3319321625

**Category:**Mathematics

**Page:**543

**View:**9937

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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

**Author**: Michael S. Weiss, Bruce E. Williams

**Publisher:**American Mathematical Soc.

**ISBN:**147040981X

**Category:**Mathematics

**Page:**110

**View:**9502

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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

**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:**9154

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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.

## Algebraic and Geometric Topology

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Algebraic topology

**Page:**N.A

**View:**8546

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## Bulletin (new Series) of the American Mathematical Society

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**6270

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## Surgery on Compact Manifolds

**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:**2381

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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.

## Annals of Mathematics Studies

**Author**: Friedhelm Waldhausen

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mappings (Mathematics)

**Page:**184

**View:**5613

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## Russian Mathematical Surveys

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematicians

**Page:**N.A

**View:**8828

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## Geometry & Topology

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Geometry

**Page:**N.A

**View:**7023

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

## BPR

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**American literature

**Page:**N.A

**View:**571

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## Manifolds and Modular Forms

**Author**: Friedrich Hirzebruch

**Publisher:**Springer-Verlag

**ISBN:**3663140458

**Category:**Mathematics

**Page:**212

**View:**1235

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## Poincarés Vermutung

*die Geschichte eines mathematischen Abenteuers*

**Author**: Donal O'Shea

**Publisher:**N.A

**ISBN:**9783596176632

**Category:**

**Page:**376

**View:**7143

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## Lehr- und Wanderjahre eines Mathematikers

*Aus dem Französischen von Theresia Übelhör*

**Author**: André Weil

**Publisher:**Springer-Verlag

**ISBN:**3034850476

**Category:**Science

**Page:**212

**View:**3093

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Mein Leben, oder zumindest das, was diesen Namen verdient -ein außer gewöhnlich glückliches Leben mit einigen Schicksalsschlägen -erstreckte sich auf die Zeit zwischen dem 6. Mai 1906, dem Tag meiner Geburt, und dem 24. Mai 1986, dem Todestag meiner Frau und Gefährtin Eveline. Wenn auf diesen Seiten, die ihr gewidmet sind, von meiner Frau recht wenig die Rede sein wird, heißt das nicht, daß sie in meinem Leben und in meinen Gedanken einen geringen Platz eingenommen hätte. Sie war im Gegenteil, beinahe vom Tag unserer ersten Begegnung an, so eng damit verwoben, daß von mir oder von ihr zu sprechen ein und dasselbe ist. Ihre Anwesenheit beziehungsweise ihre Abwesenheit bestimmte die Textur meines ganzen Lebens. Was könnte ich anderes dazu sagen, als daß unsere Ehe eine von jenen war, die La Rochefoucauld Lügen strafen? »Fulsere vere candidi mihi soles . . . . « Ebenso wird meine Schwester kaum erwähnt werden. Es ist schon lange her, daß ich meine Erinnerungen an sie Simone Petrement mitgeteilt habe, die sie in ihre gute Biographie La vie de Simone Weil einfließen ließ, wo man viele Einzelheiten über unsere gemeinsame Kindheit erfahren kann, und es wäre unnötig, dies hier zu wiederholen. Als Kinder waren wir unzertrennlich, aber ich war der große Bruder und sie die kleine Schwester. Später waren wir selten zusammen, und meist sprachen wir in scherzhaftem Ton miteinander, denn sie hatte ein fröhliches und humorvolles Naturell, wie alle, die sie kannten, bestätigt haben.

## Lineare Funktionalanalysis

*Eine anwendungsorientierte Einführung*

**Author**: Hans Wilhelm Alt

**Publisher:**Springer-Verlag

**ISBN:**3662083868

**Category:**Mathematics

**Page:**294

**View:**1490

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## A Course on Rough Paths

*With an Introduction to Regularity Structures*

**Author**: Peter K. Friz,Martin Hairer

**Publisher:**N.A

**ISBN:**9783319083339

**Category:**

**Page:**268

**View:**605

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## Current Trends in Transformation Groups

**Author**: Anthony Bak,Masaharu Morimoto,Fumihiro Ushitaki

**Publisher:**Springer Science & Business Media

**ISBN:**9781402007835

**Category:**Mathematics

**Page:**252

**View:**451

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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.