Noncommutative Localization In Algebra And Topology PDF Download
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Author | : Andrew Ranicki |
Publisher | : Cambridge University Press |
Total Pages | : 332 |
Release | : 2006-02-09 |
Genre | : Mathematics |
ISBN | : 9780521681605 |
Download Noncommutative Localization in Algebra and Topology Book in PDF, ePub and Kindle
Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.
Author | : Department of Mathematics and Statistics Andrew Ranicki |
Publisher | : |
Total Pages | : 329 |
Release | : 2014-05-14 |
Genre | : MATHEMATICS |
ISBN | : 9781107362826 |
Download Non-Commutative Localization in Algebra and Topology Book in PDF, ePub and Kindle
An introduction to noncommutative localization and an account of the state of the art suitable for researchers and graduate students.
Author | : J. P. May |
Publisher | : University of Chicago Press |
Total Pages | : 544 |
Release | : 2012-02 |
Genre | : Mathematics |
ISBN | : 0226511782 |
Download More Concise Algebraic Topology Book in PDF, ePub and Kindle
With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.
Author | : F.M.J. van Oystaeyen |
Publisher | : Springer |
Total Pages | : 408 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540386017 |
Download Non-commutative Algebraic Geometry Book in PDF, ePub and Kindle
Author | : Freddy Van Oystaeyen |
Publisher | : CRC Press |
Total Pages | : 310 |
Release | : 2000-06-06 |
Genre | : Mathematics |
ISBN | : 9780824704247 |
Download Algebraic Geometry for Associative Algebras Book in PDF, ePub and Kindle
This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level.
Author | : Christian Ausoni |
Publisher | : American Mathematical Soc. |
Total Pages | : 274 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821848399 |
Download Alpine Perspectives on Algebraic Topology Book in PDF, ePub and Kindle
Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.
Author | : Carles Broto |
Publisher | : Birkhäuser |
Total Pages | : 405 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034890184 |
Download Algebraic Topology: New Trends in Localization and Periodicity Book in PDF, ePub and Kindle
Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.
Author | : Alain Connes |
Publisher | : Springer |
Total Pages | : 364 |
Release | : 2003-12-15 |
Genre | : Mathematics |
ISBN | : 3540397027 |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author | : Jara Pascual |
Publisher | : CRC Press |
Total Pages | : 260 |
Release | : 1995-11-30 |
Genre | : Mathematics |
ISBN | : 9780582273726 |
Download Localization and Sheaves Book in PDF, ePub and Kindle
This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees property, Ore sets and the second layer condition. The first part of the book is introductory and self-contained, and might serve as a starting course (at graduate level) on localization theory within Grothendieck categories. The second part is more specialised and provides the basic machinery needed to effectively these structure sheaves, as well as to study their functorial behaviour. In this way, the book should be viewed as a first introduction to what should be called relative noncommutative algebraic geometry.
Author | : J. P. May |
Publisher | : University of Chicago Press |
Total Pages | : 262 |
Release | : 1999-09 |
Genre | : Mathematics |
ISBN | : 9780226511832 |
Download A Concise Course in Algebraic Topology Book in PDF, ePub and Kindle
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.