Topology II

Topology II
Author :
Publisher : Springer Science & Business Media
Total Pages : 264
Release :
ISBN-10 : 9783662105818
ISBN-13 : 3662105810
Rating : 4/5 (18 Downloads)

Synopsis Topology II by : D.B. Fuchs

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

Stable Homotopy and Generalised Homology

Stable Homotopy and Generalised Homology
Author :
Publisher : University of Chicago Press
Total Pages : 384
Release :
ISBN-10 : 9780226005249
ISBN-13 : 0226005240
Rating : 4/5 (49 Downloads)

Synopsis Stable Homotopy and Generalised Homology by : John Frank Adams

J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.

Algebraic Topology

Algebraic Topology
Author :
Publisher : European Mathematical Society
Total Pages : 584
Release :
ISBN-10 : 3037190485
ISBN-13 : 9783037190487
Rating : 4/5 (85 Downloads)

Synopsis Algebraic Topology by : Tammo tom Dieck

This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.

Algebraic Topology

Algebraic Topology
Author :
Publisher : Courier Corporation
Total Pages : 414
Release :
ISBN-10 : 0486691314
ISBN-13 : 9780486691312
Rating : 4/5 (14 Downloads)

Synopsis Algebraic Topology by : C. R. F. Maunder

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.

Topology and Geometry

Topology and Geometry
Author :
Publisher : Springer Science & Business Media
Total Pages : 580
Release :
ISBN-10 : 9780387979267
ISBN-13 : 0387979263
Rating : 4/5 (67 Downloads)

Synopsis Topology and Geometry by : Glen E. Bredon

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

On Homotopy

On Homotopy
Author :
Publisher :
Total Pages : 52
Release :
ISBN-10 : UOM:39015095258086
ISBN-13 :
Rating : 4/5 (86 Downloads)

Synopsis On Homotopy by : Ioan James

Algebraic Topology - Homotopy and Homology

Algebraic Topology - Homotopy and Homology
Author :
Publisher : Springer
Total Pages : 541
Release :
ISBN-10 : 9783642619236
ISBN-13 : 3642619231
Rating : 4/5 (36 Downloads)

Synopsis Algebraic Topology - Homotopy and Homology by : Robert M. Switzer

From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews

Lectures on Algebraic Topology

Lectures on Algebraic Topology
Author :
Publisher : Springer Science & Business Media
Total Pages : 389
Release :
ISBN-10 : 9783662007563
ISBN-13 : 3662007568
Rating : 4/5 (63 Downloads)

Synopsis Lectures on Algebraic Topology by : Albrecht Dold

This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica tions of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions.

An Introduction to Manifolds

An Introduction to Manifolds
Author :
Publisher : Springer Science & Business Media
Total Pages : 426
Release :
ISBN-10 : 9781441974006
ISBN-13 : 1441974008
Rating : 4/5 (06 Downloads)

Synopsis An Introduction to Manifolds by : Loring W. Tu

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

The Wild World of 4-Manifolds

The Wild World of 4-Manifolds
Author :
Publisher : American Mathematical Soc.
Total Pages : 642
Release :
ISBN-10 : 9780821837498
ISBN-13 : 0821837494
Rating : 4/5 (98 Downloads)

Synopsis The Wild World of 4-Manifolds by : Alexandru Scorpan

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.