Download or read book Classifying Spaces and Fibrations written by J. Peter May and published by American Mathematical Soc.. This book was released on 1975 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic theory of fibrations is generalized to a context in which fibres, and maps on fibres, are constrained to lie in any preassigned category of spaces [script capital] F. Then axioms are placed on [script capital] F to allow the development of a theory of associated principal fibrations and, under several choices of additional hypotheses on [script capital] F, a classification theorem is proven for such fibrations.
Download or read book Equivariant Classifying Spaces and Fibrations written by Stefan Waner and published by . This book was released on 1978 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fibrations and Their Classification written by Petar Pavešić and published by . This book was released on 2013 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of fibration is one of the great unifying mathematical ideas. It was initially introduced around 1930 in geometry and topology, and gradually expanded into many other parts of mathematics. Together with fibre bundles (which precedeed fibrations), they give formal expression to the idea of a continuous family of spaces, and of operations on such families. This monograph contains an exposition of the fundamental ideas of the theory of fibrations with particular emphasis on their classification. It deals at length with various types of fibrations as defined by Hurewicz, Dold and Serre, as well as the quasifibrations of Dold and Thom. The relationship between these concepts is analyzed in depth, with examples and counter-examples given. One of the salient properties of fibre bundles is that they are classified by homotopy classes of maps into some special spaces called classifying spaces. The classifying theory for fibrations is presented both abstractly, through the theory of representable functors, and constructively, by describing various models, like those introduced by Dold and Lashof, and by Milgram and Steenrod. In the couple of decades following their intoduction, the growth of the theory of fibrations resulted in a plethora of similar and interrelated theories and classification results for vector bundles, general fibre bundles, and other types of fibre spaces. As a new organizational principle, Peter May invented the concept of F-fibrations that generalizes all of the above, and is at the same time sufficiently structured to admit workable classification objects. The second part of the book is dedicated to an in-depth discussion of the theory of F-fibrations. The book is reasonably self-contained and the reader is assumed to have only some knowledge of general topology and basic homotopy theory, including elementary properties of homotopy groups. However, one must be aware that the level of exposition is at some places more advanced, and for these a prior course in algebraic topology or in the theory of fibre bundles would be very helpful, both as a motivation for the problems that are studied, as well as a measure of the required mathematical sophistication. The book can be used both as a text-book or as a reference. Most chapters are concluded with historical notes, tracing the origins of the concepts and the developments related to the classification of fibre bundles and fibrations.
Download or read book Fibrations of Classifying Spaces written by Kenshi Ishiguro and published by . This book was released on 1992 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classifying Spaces and Classifying Topoi written by Izak Moerdijk and published by Springer. This book was released on 2006-11-14 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces. The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.
Download or read book Fibrations of Classifying Spaces written by K. Ishiguro and published by . This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Topology of Fibre Bundles written by Norman Earl Steenrod and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Download or read book H Spaces written by Francois Sigrist and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Download or read book Cubical Homotopy Theory written by Brian A. Munson and published by Cambridge University Press. This book was released on 2015-10-06 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Download or read book Counterexamples in Topology written by Lynn Arthur Steen and published by Courier Corporation. This book was released on 2013-04-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Download or read book Homotopy Limits Completions and Localizations written by A. K. Bousfield and published by Springer. This book was released on 2009-03-20 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X. For R=Zp and X subject to usual finiteness condition, the R-completion coincides up to homotopy, with the p-profinite completion of Quillen and Sullivan; for R a subring of the rationals, the R-completion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. In part II of these notes, the authors have assembled some results on towers of fibrations, cosimplicial spaces and homotopy limits which were needed in the discussions of part I, but which are of some interest in themselves.
Download or read book The Convenient Setting of Global Analysis written by Andreas Kriegl and published by American Mathematical Soc.. This book was released on 1997 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book The Geometry of Iterated Loop Spaces written by J.P. May and published by Springer. This book was released on 2006-11-15 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Algebraic Topology written by I.M. James and published by Elsevier. This book was released on 1995-07-18 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
Download or read book Model Categories and Their Localizations written by Philip S. Hirschhorn and published by American Mathematical Soc.. This book was released on 2003 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences, i.e., by creating a new category in which the weak equivalences are isomorphisms. Quillen defined a model category to be a category together with a class of weak equivalences and additional structure useful for describing the homotopy category in terms of the original category. This allows you to make constructions analogous to those used to study the homotopy theory of topological spaces. A model category has a class of maps called weak equivalences plus two other classes of maps, called cofibrations and fibrations. Quillen's axioms ensure that the homotopy category exists and that the cofibrations and fibrations have extension and lifting properties similar to those of cofibration and fibration maps of topological spaces. During the past several decades the language of model categories has become standard in many areas of algebraic topology, and it is increasingly being used in other fields where homotopy theoretic ideas are becoming important, including modern algebraic $K$-theory and algebraic geometry. All these subjects and more are discussed in the book, beginning with the basic definitions and giving complete arguments in order to make the motivations and proofs accessible to the novice. The book is intended for graduate students and research mathematicians working in homotopy theory and related areas.
