Zur Startseite gehen
0,00 €*
Cover: 9781461287490 | Classical Topology and Combinatorial Group Theory | John Stillwell
Dekorationsartikel gehören nicht zum Leistungsumfang.
Classical Topology and Combinatorial Group Theory
Taschenbuch von John Stillwell
Sprache: Englisch

74,89 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Aktuell nicht verfügbar

Kategorien:
Beschreibung
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec­ tions to other parts of mathematics which make topology an important as well as a beautiful subject.
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec­ tions to other parts of mathematics which make topology an important as well as a beautiful subject.
Zusammenfassung
This is a well-balanced introduction to topology that stresses geometric aspects. Focusing on historical background and visual interpretation of results, it emphasizes spaces with few dimensions, where visualization is possible, and interaction with combinatorial group theory via the fundamental group. It also present algorithms for topological problems. Most of the results and proofs are known, but some have been simplified or placed in a new perspective.
Inhaltsverzeichnis
0 Introduction and Foundations.- 0.1 The Fundamental Concepts and Problems of Topology.- 0.2 Simplicial Complexes.- 0.3 The Jordan Curve Theorem.- 0.4 Algorithms.- 0.5 Combinatorial Group Theory.- 1 Complex Analysis and Surface Topology.- 1.1 Riemann Surfaces.- 1.2 Nonorientable Surfaces.- 1.3 The Classification Theorem for Surfaces.- 1.4 Covering Surfaces.- 2 Graphs and Free Groups.- 2.1 Realization of Free Groups by Graphs.- 2.2 Realization of Subgroups.- 3 Foundations for the Fundamental Group.- 3.1 The Fundamental Group.- 3.2 The Fundamental Group of the Circle.- 3.3 Deformation Retracts.- 3.4 The Seifert-Van Kampen Theorem.- 3.5 Direct Products.- 4 Fundamental Groups of Complexes.- 4.1 Poincaré's Method for Computing Presentations.- 4.2 Examples.- 4.3 Surface Complexes and Subgroup Theorems.- 5 Homology Theory and Abelianization.- 5.1 Homology Theory.- 5.2 The Structure Theorem for Finitely Generated Abelian Groups.- 5.3 Abelianization.- 6 Curves on Surfaces.- 6.1 Dehn's Algorithm.- 6.2 Simple Curves on Surfaces.- 6.3 Simplification of Simple Curves by Homeomorphisms.- 6.4 The Mapping Class Group of the Torus.- 7 Knots and Braids.- 7.1 Dehn and Schreier's Analysis of the Torus Knot Groups.- 7.2 Cyclic Coverings.- 7.3 Braids.- 8 Three-Dimensional Manifolds.- 8.1 Open Problems in Three-Dimensional Topology.- 8.2 Polyhedral Schemata.- 8.3 Heegaard Splittings.- 8.4 Surgery.- 8.5 Branched Coverings.- 9 Unsolvable Problems.- 9.1 Computation.- 9.2 HNN Extensions.- 9.3 Unsolvable Problems in Group Theory.- 9.4 The Homeomorphism Problem.- Bibliography and Chronology.
Details
Erscheinungsjahr: 2011
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xii
336 S.
ISBN-13: 9781461287490
ISBN-10: 1461287499
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Stillwell, John
Auflage: 2nd ed. 1993. Softcover reprint of the original 2nd ed. 1993
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 20 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 01.10.2011
Gewicht: 0,534 kg
Artikel-ID: 106364358
Zusammenfassung
This is a well-balanced introduction to topology that stresses geometric aspects. Focusing on historical background and visual interpretation of results, it emphasizes spaces with few dimensions, where visualization is possible, and interaction with combinatorial group theory via the fundamental group. It also present algorithms for topological problems. Most of the results and proofs are known, but some have been simplified or placed in a new perspective.
Inhaltsverzeichnis
0 Introduction and Foundations.- 0.1 The Fundamental Concepts and Problems of Topology.- 0.2 Simplicial Complexes.- 0.3 The Jordan Curve Theorem.- 0.4 Algorithms.- 0.5 Combinatorial Group Theory.- 1 Complex Analysis and Surface Topology.- 1.1 Riemann Surfaces.- 1.2 Nonorientable Surfaces.- 1.3 The Classification Theorem for Surfaces.- 1.4 Covering Surfaces.- 2 Graphs and Free Groups.- 2.1 Realization of Free Groups by Graphs.- 2.2 Realization of Subgroups.- 3 Foundations for the Fundamental Group.- 3.1 The Fundamental Group.- 3.2 The Fundamental Group of the Circle.- 3.3 Deformation Retracts.- 3.4 The Seifert-Van Kampen Theorem.- 3.5 Direct Products.- 4 Fundamental Groups of Complexes.- 4.1 Poincaré's Method for Computing Presentations.- 4.2 Examples.- 4.3 Surface Complexes and Subgroup Theorems.- 5 Homology Theory and Abelianization.- 5.1 Homology Theory.- 5.2 The Structure Theorem for Finitely Generated Abelian Groups.- 5.3 Abelianization.- 6 Curves on Surfaces.- 6.1 Dehn's Algorithm.- 6.2 Simple Curves on Surfaces.- 6.3 Simplification of Simple Curves by Homeomorphisms.- 6.4 The Mapping Class Group of the Torus.- 7 Knots and Braids.- 7.1 Dehn and Schreier's Analysis of the Torus Knot Groups.- 7.2 Cyclic Coverings.- 7.3 Braids.- 8 Three-Dimensional Manifolds.- 8.1 Open Problems in Three-Dimensional Topology.- 8.2 Polyhedral Schemata.- 8.3 Heegaard Splittings.- 8.4 Surgery.- 8.5 Branched Coverings.- 9 Unsolvable Problems.- 9.1 Computation.- 9.2 HNN Extensions.- 9.3 Unsolvable Problems in Group Theory.- 9.4 The Homeomorphism Problem.- Bibliography and Chronology.
Details
Erscheinungsjahr: 2011
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xii
336 S.
ISBN-13: 9781461287490
ISBN-10: 1461287499
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Stillwell, John
Auflage: 2nd ed. 1993. Softcover reprint of the original 2nd ed. 1993
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 20 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 01.10.2011
Gewicht: 0,534 kg
Artikel-ID: 106364358
Warnhinweis

Ähnliche Produkte

Ähnliche Produkte

Taschenbuch
Cover: 9780521090612 | Generalized Hypergeometric Functions | Lucy Joan Slater | Taschenbuch
Generalized Hypergeometric Functions
EAN: 9780521090612
Sprache: Englisch
Von/Mit: Lucy Joan Slater

48,65 €*

Lieferzeit 1-2 Wochen

Taschenbuch
Cover: 9783540629504 | Rewriting Techniques and Applications | Hubert Comon | Taschenbuch
Rewriting Techniques and Applications
8th International Conference, RTA-97, Sitges, Spain, June 2-5, 1997. Proceedings
EAN: 9783540629504
Sprache: Englisch
Von/Mit: Hubert Comon

56,65 €*

Lieferzeit 4-7 Werktage

Taschenbuch
Cover: 9783540343943 | Algèbre commutative | Chapitre 10 | N. Bourbaki | Taschenbuch | 2006
Algèbre commutative
Chapitre 10
EAN: 9783540343943
Sprache: Französisch
Von/Mit: N. Bourbaki

53,49 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783540520252 | Statistische Methoden 2 | Planung und Auswertung | Lothar Sachs | Buch
Statistische Methoden 2
Planung und Auswertung
EAN: 9783540520252
Sprache: Deutsch
Von/Mit: Lothar Sachs

32,99 €*

Lieferzeit 4-7 Werktage

Buch
Cover: 9789814374682 | INTRO SEMI-TENSOR PRODUCT MATRICE & APPL | Cheng | Buch | Englisch
INTRO SEMI-TENSOR PRODUCT MATRICE & APPL
EAN: 9789814374682
Sprache: Englisch
Von/Mit: Hongsheng Qi & Yin Zhao Daizhan Cheng

233,95 €*

Lieferzeit 1-2 Wochen

Taschenbuch
Cover: 9781441928191 | Basic Topology | M. A. Armstrong | Taschenbuch | Paperback | xii
Basic Topology
EAN: 9781441928191
Sprache: Englisch
Von/Mit: M. A. Armstrong

58,84 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9789048143368 | Introduction to Geometry of Manifolds with Symmetry | V. V. Trofimov
Introduction to Geometry of Manifolds with Symmetry
EAN: 9789048143368
Sprache: Englisch
Von/Mit: V. V. Trofimov

106,99 €*

Aktuell nicht verfügbar

Buch
Cover: 9783486241792 | Lexikon der Statistik | Nachschlagewerk für Anwender | Karl Bosch
Lexikon der Statistik
Nachschlagewerk für Anwender
EAN: 9783486241792
Sprache: Deutsch
Von/Mit: Karl Bosch

109,95 €*

Aktuell nicht verfügbar

Buch
Cover: 9789811301452 | Generalized Inverses: Theory and Computations | Guorong Wang (u. a.)
Generalized Inverses: Theory and Computations
EAN: 9789811301452
Sprache: Englisch
Von/Mit: Guorong Wang (u. a.)

128,39 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783030282967 | Introduction to ¿²-invariants | Holger Kammeyer | Taschenbuch | viii
Introduction to ¿²-invariants
EAN: 9783030282967
Sprache: Englisch
Von/Mit: Holger Kammeyer

53,49 €*

Aktuell nicht verfügbar

Buch
Cover: 9783662652763 | Geometry of Continued Fractions | Oleg N. Karpenkov | Buch | xx | 2022
Geometry of Continued Fractions
EAN: 9783662652763
Sprache: Englisch
Von/Mit: Oleg N. Karpenkov

74,89 €*

Aktuell nicht verfügbar

Diese Website verwendet Cookies, um eine bestmögliche Erfahrung bieten zu können. Mehr Informationen ...