Bridging Algebra Geometry And Topology

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Bridging Algebra, Geometry, and Topology

Denis Ibadula,Willem Veys
Bridging Algebra Geometry and Topology Book PDF

Author : Denis Ibadula,Willem Veys
Publisher : Springer
Page : 295 pages
File Size : 55,7 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9783319091860

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Bridging Algebra, Geometry, and Topology by Denis Ibadula,Willem Veys Pdf

Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

Lecture Notes in Algebraic Topology

James Frederic Davis,Paul Kirk
Lecture Notes in Algebraic Topology Book PDF

Author : James Frederic Davis,Paul Kirk
Publisher : Unknown
Page : 367 pages
File Size : 41,9 Mb
Release : 2001
Category : Algebraic topology
ISBN : 1470420880

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Lecture Notes in Algebraic Topology by James Frederic Davis,Paul Kirk Pdf

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.

Algebraic Topology Via Differential Geometry

M. Karoubi,C. Leruste
Algebraic Topology Via Differential Geometry Book PDF

Author : M. Karoubi,C. Leruste
Publisher : Cambridge University Press
Page : 380 pages
File Size : 55,8 Mb
Release : 1987
Category : Mathematics
ISBN : 0521317142

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Algebraic Topology Via Differential Geometry by M. Karoubi,C. Leruste Pdf

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

Topology and Geometry

Glen E. Bredon
Topology and Geometry Book PDF

Author : Glen E. Bredon
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 40,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475768480

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Topology and Geometry by Glen E. Bredon Pdf

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

Algebraic Topology

Clark Bray,Adrian Butscher,Simon Rubinstein-Salzedo
Algebraic Topology Book PDF

Author : Clark Bray,Adrian Butscher,Simon Rubinstein-Salzedo
Publisher : Springer Nature
Page : 216 pages
File Size : 54,8 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.

Issues in Algebra, Geometry, and Topology: 2011 Edition

Anonim
Issues in Algebra Geometry and Topology 2011 Edition Book PDF

Author : Anonim
Publisher : ScholarlyEditions
Page : 395 pages
File Size : 41,9 Mb
Release : 2012-01-09
Category : Mathematics
ISBN : 9781464966354

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Issues in Algebra, Geometry, and Topology: 2011 Edition by Anonim Pdf

Issues in Algebra, Geometry, and Topology / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Algebra, Geometry, and Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Algebra, Geometry, and Topology in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Introduction to Topology

Tej Bahadur Singh
Introduction to Topology Book PDF

Author : Tej Bahadur Singh
Publisher : Springer
Page : 452 pages
File Size : 43,5 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9789811369544

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Introduction to Topology by Tej Bahadur Singh Pdf

Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.

Topology

Solomon Lefschetz
Topology Book PDF

Author : Solomon Lefschetz
Publisher : American Mathematical Soc.
Page : 428 pages
File Size : 52,6 Mb
Release : 1930-12-31
Category : Mathematics
ISBN : 9780821846032

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Topology by Solomon Lefschetz Pdf

Lefschetz's Topology was written in the period in between the beginning of topology, by Poincare, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of algebraic varieties. He also gives applications to vector distributions, complex spaces, and Kronecker's characteristic theory.

Algebraic Topology

Edwin H. Spanier
Algebraic Topology Book PDF

Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 52,9 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.

A Geometric Introduction to Topology

Charles Terence Clegg Wall
A Geometric Introduction to Topology Book PDF

Author : Charles Terence Clegg Wall
Publisher : Courier Corporation
Page : 195 pages
File Size : 47,6 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 9780486678504

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A Geometric Introduction to Topology by Charles Terence Clegg Wall Pdf

First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.

Algebraic Topology: A Structural Introduction

Marco Grandis
Algebraic Topology A Structural Introduction Book PDF

Author : Marco Grandis
Publisher : World Scientific
Page : 372 pages
File Size : 43,8 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.

Topology Through Inquiry

Michael Starbird,Francis Su
Topology Through Inquiry Book PDF

Author : Michael Starbird,Francis Su
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 42,6 Mb
Release : 2020-09-10
Category : Education
ISBN : 9781470462611

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Topology Through Inquiry by Michael Starbird,Francis Su Pdf

Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.

Handbook of Geometry and Topology of Singularities I

José Luis Cisneros Molina,Dũng Tráng Lê,José Seade
Handbook of Geometry and Topology of Singularities I Book PDF

Author : José Luis Cisneros Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 616 pages
File Size : 48,6 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030530617

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Handbook of Geometry and Topology of Singularities I by José Luis Cisneros Molina,Dũng Tráng Lê,José Seade Pdf

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Topology

Paul L. Shick
Topology Book PDF

Author : Paul L. Shick
Publisher : John Wiley & Sons
Page : 291 pages
File Size : 49,8 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118030585

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Topology by Paul L. Shick Pdf

The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs

Perspectives on Projective Geometry

Jürgen Richter-Gebert
Perspectives on Projective Geometry Book PDF

Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 49,6 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783642172861

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Perspectives on Projective Geometry by Jürgen Richter-Gebert Pdf

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.