Geometry of Loop Spaces and the Cobar Construction PDF Download
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Author: Hans J. Baues
Publisher: American Mathematical Soc.
ISBN: 0821822306
Category : Mathematics
Languages : en
Pages : 194
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Book Description
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: Hans J. Baues
Publisher: American Mathematical Soc.
ISBN: 0821822306
Category : Mathematics
Languages : en
Pages : 194
Get Book Here
Book Description
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: Hans Joachim Baues
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: I.M. James
Publisher: Elsevier
ISBN: 0080532985
Category : Mathematics
Languages : en
Pages : 1336
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Book Description
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: Justin R. Smith
Publisher: American Mathematical Soc.
ISBN: 0821825887
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This paper develops a new invariant of a CW-complex called the m-structure and uses it to perform homotopy-theoretic computations. The m-structure of a space encapsulates the coproduct structure, as well as higher-coproduct structures that determine Steenrod-operations. Given an m-structure on the chain complex of a reduced simplicial complex of a pointed simply-connected space, one can equip the cobar construction of this chain-complex with a natural m-structure. This result allows one to form iterated cobar constructions that are shown to be homotopy equivalent to iterated loop-spaces.
Author: William Joseph Haboush
Publisher: American Mathematical Soc.
ISBN: 0821815415
Category : Mathematics
Languages : en
Pages : 429
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Book Description
Proceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general
Author: Jesus De Loera
Publisher: Springer Science & Business Media
ISBN: 3642129714
Category : Mathematics
Languages : en
Pages : 547
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Book Description
Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.
Author: James D. Stasheff
Publisher: American Mathematical Soc.
ISBN: 082180913X
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas.
Author: Shiing-Shen Chern
Publisher: American Mathematical Soc.
ISBN: 082180247X
Category : Geometry, Differential
Languages : en
Pages : 463
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Book Description
Author: Hans J. Baues
Publisher: Oxford University Press
ISBN: 9780198514824
Category : Mathematics
Languages : en
Pages : 524
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Book Description
This monograph represents an attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classifications, and includes applications to the classification of manifolds.
Author: Folkert Müller-Hoissen
Publisher: Springer Science & Business Media
ISBN: 3034804059
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations.
