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Author : Janko Latschev
Publisher :
ISBN 13 : 9783037196533
Total Pages : 494 pages
Book Rating : 4.1/5 (965 download)
Download or read book Free Loop Spaces in Geometry and Topology written by Janko Latschev and published by . This book was released on 2015 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 : Edward R. Fadell
Publisher : Springer Science & Business Media
ISBN 13 : 3642564461
Total Pages : 314 pages
Book Rating : 4.6/5 (425 download)
Download or read book Geometry and Topology of Configuration Spaces written by Edward R. Fadell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.
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.P. May
Publisher : Springer
ISBN 13 : 9783540059042
Total Pages : 175 pages
Book Rating : 4.0/5 (59 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 1989-10-01 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 : Hans J. Baues
Publisher : American Mathematical Soc.
ISBN 13 : 0821822306
Total Pages : 194 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 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.
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 : John Frank Adams
Publisher : Princeton University Press
ISBN 13 : 0691082065
Total Pages : 228 pages
Book Rating : 4.6/5 (91 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 228 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 : Ralph L. Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3764373881
Total Pages : 159 pages
Book Rating : 4.7/5 (643 download)
Download or read book String Topology and Cyclic Homology written by Ralph L. Cohen and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant 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.
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 : 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 : Michael Davis
Publisher : Princeton University Press
ISBN 13 : 0691131384
Total Pages : 601 pages
Book Rating : 4.6/5 (911 download)
Download or read book The Geometry and Topology of Coxeter Groups written by Michael Davis and published by Princeton University Press. This book was released on 2008 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Author : Armen G. Sergeev
Publisher :
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.:/5 (676 download)
Download or read book Kahler Geometry of Loop Spaces written by Armen G. Sergeev and published by . This book was released on 2008 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662217392
Total Pages : 467 pages
Book Rating : 4.6/5 (622 download)
Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.
