Books about Homotopy from Amazon.com

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory.

Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master."

Milnor has published five books with Princeton University Press.

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Price: $39.98 [Notify me when price goes down.]

This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology..
Price: $44.32 [Notify me when price goes down.]

Describes topologically stable patterns such as vortices, disinclinations, dislocations, and domain walls in ordered media (superfluids, liquid and solid crystals, magnets). It also introduces the basic notions of homotopic group theory and the necessary algebraic topology constructions. The author is one of the inventors of topological classification of defects in a theory of ordered media and this classic paper provides an excellent reference text for postgraduates and researchers..
Price: $65.09 [Notify me when price goes down.]

This text is based on a one-semester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The notes are divided into two parts: prerequisites and the course proper.

Part I, the prerequisites, contains a review of material often taught in a first course in algebraic topology. It should provide a useful summary for students and non-specialists who are interested in learning the basics of algebraic topology. Included are some basic category theory, point set topology, the fundamental group, homological algebra, singular and cellular homology, and Poincaré duality.

Part II covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, spectral sequences, localization, generalized homology, and cohomology operations..
Price: $54.00 [Notify me when price goes down.]

The subject of this book is string topology, Hochschild and cyclic homology The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. The book provides many references for the reader wishing to learn more about the subject, to which it gives a perfect introduction. It is therefore suitable for both graduate students and established researchers. It is certainly the best source of much information that was until now available only to specialists and covers material from the elementary bases to the most recent developments.

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Price: $24.70 [Notify me when price goes down.]

Revised, updated, and expanded throughout, this edition of Fundamentals of Pattern Recognition addresses the field of PR from a basic mathematical view-point - treating algebraic, topological, and categorical approaches of PR using concepts from homotopy, shape, and fibre spaces theories as well as computational topology.;Maintaining the features of the first edition, this resource: provides a new section on fibrewise topology that formalizes, for the first time, multicoloured, different gray level pictures and other complex signals consisting of base and value spaces and their interconnections; explores new artificial intelligence problems on the possible interplay between recursion theory and fibrewise image topology in connection with effectiveness and decidability problems; develops original techniques and results, such as the study of extremely irregular shapes by means of the mathematical theory of shape, finite topological spaces, and category theory's applications to PR; exhibits new figures of panoramic hierarchical classifications of all mathematical approaches to PR discussed; and presents five appendices that give quick overviews of dominant concepts in PR and related fields.;Containing open research and development problems to reinforce important methodologies, this second edition of Fundamentals of Pattern Recognition is a guide for applied mathematicians; electrical and electronics, systems, and computer engineers; computer scientists; and upper-level undergraduate and graduate students in applied mathematics and computer science courses in pattern recognition theory and artificial intelligence..
Price: $122.33 [Notify me when price goes down.]

Rational homotopy is a very powerful tool for differential topology and geometry This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kahler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods..
Price: $95.43 [Notify me when price goes down.]

This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin-Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest..
Price: $39.98 [Notify me when price goes down.]