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Author : J.P. May
Publisher : Springer
ISBN 13 : 3540376038
Total Pages : 184 pages
Book Rating : 4.5/5 (43 download)
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:
Author : J. Peter May
Publisher :
ISBN 13 :
Total Pages : 175 pages
Book Rating : 4.:/5 (72 download)
Download or read book The Geometry of Iterated Loop Spaces written by J. Peter May and published by . This book was released on 1972 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Peter May
Publisher : Springer
ISBN 13 : 9780387059044
Total Pages : 175 pages
Book Rating : 4.0/5 (59 download)
Download or read book The Geometry of Iterated Loop Spaces written by J. Peter May and published by Springer. This book was released on 1972 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : F. R. Cohen
Publisher : Springer
ISBN 13 : 3540379851
Total Pages : 501 pages
Book Rating : 4.5/5 (43 download)
Download or read book The Homology of Iterated Loop Spaces written by F. R. Cohen and published by Springer. This book was released on 2007-01-05 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : F. R. Cohen
Publisher :
ISBN 13 : 9783662209226
Total Pages : 508 pages
Book Rating : 4.2/5 (92 download)
Download or read book The Homology of Iterated Loop Spaces written by F. R. Cohen and published by . This book was released on 2014-01-15 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frederick Ronald Cohen
Publisher : Springer
ISBN 13 : 9780387079844
Total Pages : 490 pages
Book Rating : 4.0/5 (798 download)
Download or read book The Homology of Iterated Loop Spaces written by Frederick Ronald Cohen and published by Springer. This book was released on 1976 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hans J. Baues
Publisher : American Mathematical Soc.
ISBN 13 : 0821822306
Total Pages : 171 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometry of Loop Spaces and the Cobar Construction written by Hans J. Baues and published by American Mathematical Soc.. This book was released on 1980 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Luc Brylinski
Publisher : Springer Science & Business Media
ISBN 13 : 0817647317
Total Pages : 318 pages
Book Rating : 4.8/5 (176 download)
Download or read book Loop Spaces, Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2009-12-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Author : John Frank Adams
Publisher : Princeton University Press
ISBN 13 : 9780691082066
Total Pages : 232 pages
Book Rating : 4.0/5 (82 download)
Download or read book Infinite Loop Spaces written by John Frank Adams and published by Princeton University Press. This book was released on 1978-09-21 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.
Author : Jeffrey Strom
Publisher : American Mathematical Society
ISBN 13 : 1470471639
Total Pages : 862 pages
Book Rating : 4.4/5 (74 download)
Download or read book Modern Classical Homotopy Theory written by Jeffrey Strom and published by American Mathematical Society. This book was released on 2023-01-19 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Author : Robert J. Wellington
Publisher : American Mathematical Soc.
ISBN 13 : 0821822586
Total Pages : 237 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Unstable Adams Spectral Sequence for Free Iterated Loop Spaces written by Robert J. Wellington and published by American Mathematical Soc.. This book was released on 1982 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The semi-stable homotopy groups of a topological space [italic]X are the unstable homotopy groups [lowercase Greek]Pi [subscript]*[capital Greek]Sigma[superscript]n[italic]X, [italic]n [greater than symbol] 0, of the suspensions of [italic]X. This monograph is concerned with computing these semi-stable homotopy groups using the unstable Adams spectral sequence for the free iterated loop spaces [capital Greek]Omega[superscript italic]n [capital Greek]Sigma[superscript italic]n [italic]X generated by [italic]X.
Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)
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.
Author : R. James Milgram
Publisher : American Mathematical Soc.
ISBN 13 : 082182063X
Total Pages : 255 pages
Book Rating : 4.8/5 (218 download)
Download or read book Topology, Geometry, and Algebra: Interactions and new directions written by R. James Milgram and published by American Mathematical Soc.. This book was released on 2001 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the conference on ``Topology, Geometry, and Algebra: Interactions and New Directions'' held in honor of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgery theory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of interaction between the different areas.
Author : I.M. James
Publisher : Elsevier
ISBN 13 : 9780080532981
Total Pages : 1324 pages
Book Rating : 4.5/5 (329 download)
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 1324 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.
Author : Martin Markl
Publisher : American Mathematical Soc.
ISBN 13 : 0821843621
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)
Download or read book Operads in Algebra, Topology and Physics written by Martin Markl and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
Author : John Frank Adams
Publisher : Princeton University Press
ISBN 13 : 1400821258
Total Pages : 230 pages
Book Rating : 4.4/5 (8 download)
Download or read book Infinite Loop Spaces (AM-90), Volume 90 written by John Frank Adams and published by Princeton University Press. This book was released on 1978-09-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.
Author : Mohammed Abouzaid
Publisher : European Mathematical Society
ISBN 13 : 9783037191538
Total Pages : 504 pages
Book Rating : 4.1/5 (915 download)
Download or read book Free Loop Spaces in Geometry and Topology written by Mohammed Abouzaid and published by European Mathematical Society. This book was released on 2015 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 1990s, two initially unrelated developments brought free loop spaces into renewed focus. In 1999, Chas and Sullivan introduced a wealth of new algebraic operations on the homology of these spaces under the name of string topology, the full scope of which is still not completely understood. A few years earlier, Viterbo had discovered a first deep link between the symplectic topology of cotangent bundles and the topology of their free loop space. In the past 15 years, many exciting connections between these two viewpoints have been found. Still, researchers working on one side of the story often know quite little about the other. One of the main purposes of this book is to facilitate communication between topologists and symplectic geometers thinking about free loop spaces. It was written by active researchers who approach the topic from both perspectives and provides a concise overview of many of the classical results. The book also begins to explore the new directions of research that have emerged recently. One highlight is the research monograph by M. Abouzaid, which proves a strengthened version of Viterbo's isomorphism between the homology of the free loop space of a manifold and the symplectic cohomology of its cotangent bundle, following a new strategy. The book grew out of a learning seminar on free loop spaces held at Strasbourg University in 2008-2009 and should be accessible to graduate students with a general interest in the topic. It focuses on introducing and explaining the most important aspects, rather than offering encyclopedic coverage, while providing the interested reader with a broad basis for further studies and research.
