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| Author | : Sadanand Verma |
| Publisher | : |
| Total Pages | : 242 |
| Release | : 1959 |
| Genre | : Homotopy theory |
| ISBN | : |
| Author | : Sadanand Verma |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1958 |
| Genre | : Homotopy theory |
| ISBN | : |
| Author | : Klaus Heiner Kamps |
| Publisher | : World Scientific |
| Total Pages | : 474 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9789810216023 |
"This book provides a thorough and well-written guide to abstract homotopy theory. It could well serve as a graduate text in this topic, or could be studied independently by someone with a background in basic algebra, topology, and category theory."
| Author | : Emily Riehl |
| Publisher | : Cambridge University Press |
| Total Pages | : 371 |
| Release | : 2014-05-26 |
| Genre | : Mathematics |
| ISBN | : 1139952633 |
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
| Author | : D. A. Edwards |
| Publisher | : Springer |
| Total Pages | : 303 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540381031 |
| Author | : Eric M. Friedlander |
| Publisher | : Princeton University Press |
| Total Pages | : 191 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881498 |
This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions. One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.
| Author | : Bjorn Ian Dundas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2007-07-11 |
| Genre | : Mathematics |
| ISBN | : 3540458972 |
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
| Author | : Birgit Richter |
| Publisher | : Cambridge University Press |
| Total Pages | : 402 |
| Release | : 2020-04-16 |
| Genre | : Mathematics |
| ISBN | : 1108847625 |
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.
| Author | : William G. Dwyer |
| Publisher | : Birkhäuser |
| Total Pages | : 106 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883560 |
This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
| Author | : Mark E. Mahowald |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821808052 |
The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
