Directed Algebraic Topology

Author : Lisbeth Fajstrup,Eric Goubault,Emmanuel Haucourt,Samuel Mimram,Martin Raussen
Publisher : Springer
Page : 167 pages
File Size : 42,6 Mb
Release : 2016-03-02
Category : Computers
ISBN : 9783319153988

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Directed Algebraic Topology and Concurrency by Lisbeth Fajstrup,Eric Goubault,Emmanuel Haucourt,Samuel Mimram,Martin Raussen Pdf

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than “just” the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.

Author : Marco Grandis
Publisher : Cambridge University Press
Page : 445 pages
File Size : 42,5 Mb
Release : 2009-09-17
Category : Mathematics
ISBN : 9781139482585

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Directed Algebraic Topology by Marco Grandis Pdf

This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenomena' and its domain should be distinguished from that of classical algebraic topology by the principle that directed spaces have privileged directions and directed paths therein need not be reversible. Its homotopical tools (corresponding in the classical case to ordinary homotopies, fundamental group and fundamental groupoid) should be similarly 'non-reversible': directed homotopies, fundamental monoid and fundamental category. Homotopy constructions occur here in a directed version, which gives rise to new 'shapes', like directed cones and directed spheres. Applications will deal with domains where privileged directions appear, including rewrite systems, traffic networks and biological systems. The most developed examples can be found in the area of concurrency.

Author : Samuel Eilenberg,Norman Steenrod
Publisher : Princeton University Press
Page : 345 pages
File Size : 52,8 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400877492

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Foundations of Algebraic Topology by Samuel Eilenberg,Norman Steenrod Pdf

The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Andrew H. Wallace
Publisher : Courier Corporation
Page : 290 pages
File Size : 50,8 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780486462394

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Algebraic Topology by Andrew H. Wallace Pdf

Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

Author : Clark Bray,Adrian Butscher,Simon Rubinstein-Salzedo
Publisher : Springer Nature
Page : 216 pages
File Size : 55,5 Mb
Release : 2021-06-18
Category : Mathematics
ISBN : 9783030706081

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Algebraic Topology by Clark Bray,Adrian Butscher,Simon Rubinstein-Salzedo Pdf

Algebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminaries needed for the formal definition of a surface. Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology. This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text. This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class. The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course.

Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493221

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Algebraic Topology by Edwin H. Spanier Pdf

This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 42,6 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

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A Concise Course in Algebraic Topology by J. P. May Pdf

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.

Author : Marco Grandis
Publisher : World Scientific
Page : 372 pages
File Size : 44,5 Mb
Release : 2021-12-24
Category : Mathematics
ISBN : 9789811248375

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Algebraic Topology: A Structural Introduction by Marco Grandis Pdf

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 R. Munkres
Publisher : CRC Press
Page : 465 pages
File Size : 51,7 Mb
Release : 2018-03-05
Category : Mathematics
ISBN : 9780429962462

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Elements Of Algebraic Topology by James R. Munkres Pdf

Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.

Author : Solomon Lefschetz
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 49,9 Mb
Release : 1942-12-31
Category : Mathematics
ISBN : 9780821810279

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Algebraic Topology by Solomon Lefschetz Pdf

Author : Marvin J. Greenberg
Publisher : CRC Press
Page : 332 pages
File Size : 47,9 Mb
Release : 2018-03-05
Category : Mathematics
ISBN : 9780429970955

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Algebraic Topology by Marvin J. Greenberg Pdf

Great first book on algebraic topology. Introduces (co)homology through singular theory.

Author : M. Glezerman
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 48,5 Mb
Release : 1962
Category : Mathematics
ISBN : 0821816071

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Algebraic Topology by M. Glezerman Pdf

Author : Allen Hatcher
Publisher : Cambridge University Press
Page : 572 pages
File Size : 48,5 Mb
Release : 2002
Category : Mathematics
ISBN : 0521795400

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Algebraic Topology by Allen Hatcher Pdf

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Author : Steven H. Weintraub
Publisher : Springer
Page : 169 pages
File Size : 41,9 Mb
Release : 2014-10-31
Category : Mathematics
ISBN : 9781493918447

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Fundamentals of Algebraic Topology by Steven H. Weintraub Pdf

This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.

Author : Haynes R Miller
Publisher : World Scientific
Page : 405 pages
File Size : 41,5 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9789811231261

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Lectures On Algebraic Topology by Haynes R Miller Pdf

Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.