Homotopy Theory via Algebraic Geometry and Group Representations PDF Download
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Author: Mark E. Mahowald
Publisher: American Mathematical Soc.
ISBN: 0821808052
Category : Mathematics
Languages : en
Pages : 394
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Book Description
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.
Author: Mark E. Mahowald
Publisher: American Mathematical Soc.
ISBN: 0821808052
Category : Mathematics
Languages : en
Pages : 394
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Book Description
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.
Author: Jeffrey Strom
Publisher: American Mathematical Soc.
ISBN: 0821852868
Category : Mathematics
Languages : en
Pages : 862
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Book Description
The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Author: K Heiner Kamps
Publisher: World Scientific
ISBN: 9814502553
Category : Mathematics
Languages : en
Pages : 476
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Book Description
The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).
Author: Neil Chriss
Publisher: Birkhauser
ISBN: 0817637923
Category : Mathematics
Languages : en
Pages : 495
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Book Description
This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.
Author: Paul Gregory Goerss
Publisher: American Mathematical Soc.
ISBN: 0821832859
Category : Mathematics
Languages : en
Pages : 520
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Book Description
As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.
Author: L. Pachter
Publisher: Cambridge University Press
ISBN: 9780521857000
Category : Mathematics
Languages : en
Pages : 440
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Book Description
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
Author: Bjorn Ian Dundas
Publisher: Springer Science & Business Media
ISBN: 3540458972
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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: Ryoshi Hotta
Publisher: Springer Science & Business Media
ISBN: 081764363X
Category : Mathematics
Languages : en
Pages : 408
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Book Description
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Author: Burt Totaro
Publisher: Cambridge University Press
ISBN: 1107015774
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Author: Emily Riehl
Publisher: Cambridge University Press
ISBN: 1139952633
Category : Mathematics
Languages : en
Pages : 371
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Book Description
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.
