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Homotopy Commutativity Of H Spaces
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Book Synopsis A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $\bmod 2$ Cohomology Rings by : Michael Slack
Download or read book A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $\bmod 2$ Cohomology Rings written by Michael Slack and published by American Mathematical Soc.. This book was released on 1991 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that a 2-connected homotopy commutative H-space with associative mod 2 homology ring and finitely generated mod 2 cohomology ring has acyclic mod 2 cohomology. This implies that a connected, homotopy commutative, homotopy associative H-space with finitely generated mod 2 cohomology ring is mod 2 homotopy equivalent to a product of Eilenberg-MacLane spaces, giving a complete classification of such spaces localized at the prime 2.
Book Synopsis Homotopy Commutativity of H-spaces by : Francis Dudley Williams
Download or read book Homotopy Commutativity of H-spaces written by Francis Dudley Williams and published by . This book was released on 1965 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy-commutativity in H-spaces by : Roy René Douglas
Download or read book Homotopy-commutativity in H-spaces written by Roy René Douglas and published by . This book was released on 1965 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hopf Spaces written by and published by Elsevier. This book was released on 1976-01-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf Spaces
Book Synopsis The Homology of Hopf Spaces by : R.M. Kane
Download or read book The Homology of Hopf Spaces written by R.M. Kane and published by North Holland. This book was released on 1988-08 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces.
Book Synopsis Handbook of Algebraic Topology by : I.M. James
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.
Book Synopsis A Concise Course in Algebraic Topology by : J. P. May
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:
Book Synopsis Groups of Homotopy Classes by : M. Arkowitz
Download or read book Groups of Homotopy Classes written by M. Arkowitz and published by Springer. This book was released on 2013-06-29 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the sets that one encounters in homotopy classification problems have a natural group structure. Among these are the groups [A,nX] of homotopy classes of maps of a space A into a loop-space nx. Other examples are furnished by the groups ~(y) of homotopy classes of homotopy equivalences of a space Y with itself. The groups [A,nX] and ~(Y) are not necessarily abelian. It is our purpose to study these groups using a numerical invariant which can be defined for any group. This invariant, called the rank of a group, is a generalisation of the rank of a finitely generated abelian group. It tells whether or not the groups considered are finite and serves to distinguish two infinite groups. We express the rank of subgroups of [A,nX] and of C(Y) in terms of rational homology and homotopy invariants. The formulas which we obtain enable us to compute the rank in a large number of concrete cases. As the main application we establish several results on commutativity and homotopy-commutativity of H-spaces. Chapter 2 is purely algebraic. We recall the definition of the rank of a group and establish some of its properties. These facts, which may be found in the literature, are needed in later sections. Chapter 3 deals with the groups [A,nx] and the homomorphisms f*: [B,n~l ~ [A,nx] induced by maps f: A ~ B. We prove a general theorem on the rank of the intersection of coincidence subgroups (Theorem 3. 3).
Book Synopsis Moduli Spaces of Riemannian Metrics by : Wilderich Tuschmann
Download or read book Moduli Spaces of Riemannian Metrics written by Wilderich Tuschmann and published by Springer. This book was released on 2015-10-14 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
Book Synopsis The Ten Types of H-spaces by : I. M. James
Download or read book The Ten Types of H-spaces written by I. M. James and published by . This book was released on 1959 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis H-Spaces from a Homotopy Point of View by : James Stasheff
Download or read book H-Spaces from a Homotopy Point of View written by James Stasheff and published by Springer. This book was released on 2006-11-15 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Une Degustation Topologique: Homotopy Theory in the Swiss Alps by : Dominique Arlettaz
Download or read book Une Degustation Topologique: Homotopy Theory in the Swiss Alps written by Dominique Arlettaz and published by American Mathematical Soc.. This book was released on 2000 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The talks given at the Arolla Conference on Algebraic Topology covered a broad spectrum of current research in homotopy theory, offering participants the possibility to sample and relish selected morsels of homotopy theory, much as a participant in a wine tasting partakes of a variety of fine wines. True to the spirit of the conference, the proceedings included in this volume present a savory sampler of homotopical delicacies. Readers will find within these pages a compilation of articles describing current research in the area, including classical stable and unstable homotopy theory, configuration spaces, group cohomology, K-theory, localization, p-compact groups, and simplicial theory.
Book Synopsis From Categories to Homotopy Theory by : Birgit Richter
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Book Synopsis A Classification Theorem for Homotopy Commutative H-spaces with Finitely Generated Mod 2 Cohomology Rings by : Michael Slack
Download or read book A Classification Theorem for Homotopy Commutative H-spaces with Finitely Generated Mod 2 Cohomology Rings written by Michael Slack and published by . This book was released on 1990 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Homotopy Theory by : Paul Selick
Download or read book Introduction to Homotopy Theory written by Paul Selick and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Book Synopsis Proceedings of the Northwestern Homotopy Theory Conference by : Haynes R. Miller
Download or read book Proceedings of the Northwestern Homotopy Theory Conference written by Haynes R. Miller and published by American Mathematical Soc.. This book was released on 1983 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:
