Lectures on Algebraic Topology PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures on Algebraic Topology PDF full book. Access full book title Lectures on Algebraic Topology by Albrecht Dold. Download full books in PDF and EPUB format.
Author: Albrecht Dold
Publisher: Springer Science & Business Media
ISBN: 3642678211
Category : Mathematics
Languages : en
Pages : 390
Get Book Here
Book Description
Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.
Author: Michael Barr
Publisher: American Mathematical Soc.
ISBN: 0821828770
Category : Mathematics
Languages : en
Pages : 194
Get Book Here
Book Description
Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background. It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology. The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.
Author: Albrecht Dold
Publisher: Springer Science & Business Media
ISBN: 3642678211
Category : Mathematics
Languages : en
Pages : 390
Get Book Here
Book Description
Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.
Author: Martin Majewski
Publisher: American Mathematical Soc.
ISBN: 0821819208
Category : Mathematics
Languages : en
Pages : 175
Get Book Here
Book Description
The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.
Author: Jean Dieudonné
Publisher: Springer Science & Business Media
ISBN: 0817649077
Category : Mathematics
Languages : en
Pages : 666
Get Book Here
Book Description
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
Author: James F. Davis
Publisher: American Mathematical Society
ISBN: 1470473682
Category : Mathematics
Languages : en
Pages : 385
Get Book Here
Book Description
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Author: Marco Grandis
Publisher: World Scientific
ISBN: 9811248370
Category : Mathematics
Languages : en
Pages : 372
Get Book Here
Book Description
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.
Author: James F. Davis and Paul Kirk
Publisher: American Mathematical Soc.
ISBN: 9780821872208
Category : Algebraic topology
Languages : en
Pages : 388
Get Book Here
Book Description
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic andgeometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, someknowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstructiontheory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to presentproofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, andhomological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Author: Vialar Thierry
Publisher: BoD - Books on Demand
ISBN: 2955199052
Category : Mathematics
Languages : en
Pages : 1134
Get Book Here
Book Description
The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
Author: Takashi Onoda
Publisher: Springer Science & Business Media
ISBN: 3642256546
Category : Computers
Languages : en
Pages : 351
Get Book Here
Book Description
This book constitutes the thoroughly refereed post-proceedings of four workshops held as satellite events of the JSAI International Symposia on Artificial Intelligence 2010, in Tokyo, Japan, in November 2010. The 28 revised full papers with four papers for the following four workshops presented were carefully reviewed and selected from 70 papers. The papers are organized in sections Logic and Engineering of Natural Language Semantics (LENLS), Juris-Informatics (JURISIN), Advanced Methodologies for Bayesian Networks (AMBN), and Innovating Service Systems (ISS).
Author: Joe Suzuki
Publisher: Springer
ISBN: 3319283790
Category : Computers
Languages : en
Pages : 281
Get Book Here
Book Description
This volume constitutes the refereed proceedings of the Second International Workshop on Advanced Methodologies for Bayesian Networks, AMBN 2015, held in Yokohama, Japan, in November 2015. The 18 revised full papers and 6 invited abstracts presented were carefully reviewed and selected from numerous submissions. In the International Workshop on Advanced Methodologies for Bayesian Networks (AMBN), the researchers explore methodologies for enhancing the effectiveness of graphical models including modeling, reasoning, model selection, logic-probability relations, and causality. The exploration of methodologies is complemented discussions of practical considerations for applying graphical models in real world settings, covering concerns like scalability, incremental learning, parallelization, and so on.
