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Umfang: XI, 207 S. : , graph. Darst.

Ausgabe: 2., rev. ed.

ISBN: 978-3-11-025035-0

Serie: De Gruyter textbook

Anmerkung: Literaturverz. S. 195 - 203

Weitere Ausg.: Erscheint auch als Online-Ausgabe ISBN 978-3-11-025036-7

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Mannigfaltigkeit ; Dimension 3 ; Topologie ; Casson-Invariante

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: Inhaltstext

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URL: http://deposit.dnb.de/cgi-bin/dokserv?id=3931257&prov=M&dok_var=1&dok_ext=htm

Mehr zum Autor: Saveliev, Nikolai, 1966-

UID:

Umfang: Online-Ressource , Online Ressource (220 S.)

Ausgabe: 2. Aufl.

ISBN: 3110250357

Inhalt: Nikolai Saveliev

Inhalt: This textbook -now in its second revised and extended edition -introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds

Anmerkung: Description based upon print version of record , 11.3 A surgery formula for the Rohlin invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 14 Representation spaces; 14.1 The topology of representation spaces; 14.2 Irreducible representations; 14.3 Representations of free groups; 14.4 Representations of surface groups; 14.5 Representations for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations. , 16.3 Independence of Heegaard splitting16.4 Exercises; 17 Casson's invariant for knots; 17.1 Preferred Heegaard splittings; 17.2 The Casson invariant for knots; 17.3 The difference cycle; 17.4 The Casson invariant for boundary links; 17.5 The Casson invariant of a trefoil; 18 An application of the Casson invariant; 18.1 Triangulating 4-manifolds; 18.2 Higher-dimensional manifolds; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index;. , 4 Even surgeries4.1 Exercises; 5 Review of 4-manifolds; 5.1 Definition of the intersection form; 5.2 The unimodular integral forms; 5.3 Four-manifolds and intersection forms; 5.4 Exercises; 6 Four-manifolds with boundary; 6.1 The intersection form; 6.2 Homology spheres via surgery on knots; 6.3 Seifert homology spheres; 6.4 The Rohlin invariant; 6.5 Exercises; 7 Invariants of knots and links; 7.1 Seifert surfaces; 7.2 Seifert matrices; 7.3 The Alexander polynomial; 7.4 Other invariants from Seifert surfaces; 7.5 Knots in homology spheres; 7.6 Boundary links and the Alexander polynomial. , 7.7 Exercises8 Fibered knots; 8.1 The definition of a fibered knot; 8.2 The monodromy; 8.3 More about torus knots; 8.4 Joins; 8.5 The monodromy of torus knots; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 10.3 Representing homology classes by surfaces; 11 The Rohlin invariant; 11.1 Definition of the Rohlin invariant; 11.2 The Rohlin invariant of Seifert spheres. , Preface; Introduction; Glossary; 1 Heegaard splittings; 1.1 Introduction; 1.2 Existence of Heegaard splittings; 1.3 Stable equivalence of Heegaard splittings; 1.4 The mapping class group; 1.5 Manifolds of Heegaard genus ‹_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 2 Dehn surgery; 2.1 Knots and links in 3-manifolds; 2.2 Surgery on links in S3; 2.3 Surgery description of lens spaces and Seifert manifolds; 2.4 Surgery and 4-manifolds; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises.

Weitere Ausg.: ISBN 3110250365

Weitere Ausg.: ISBN 9783110250367

Sprache: Englisch

Schlagwort(e): Mannigfaltigkeit ; Dimension 3 ; Niederdimensionale Topologie ; Casson-Invariante ; Electronic books ; Electronic books

DOI: 10.1515/9783110250367

URL: http://www.degruyter.com/doi/book/10.1515/9783110250367

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URL: Volltext  (lizenzpflichtig)

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URL: Cover

URL: Inhaltstext

URL: Cover

UID:

Umfang: 1 Online-Ressource (XI, 207 S.).

Ausgabe: 2. Aufl

ISBN: 978-3-11-025036-7

Serie: De Gruyter Textbook

Anmerkung: Description based upon print version of record. - Nikolai Saveliev. - This textbook -now in its second revised and extended edition -introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds

Weitere Ausg.: Erscheint auch als Online-Ausgabe ISBN 978-3-11-025035-0

Sprache: Englisch

Schlagwort(e): Mannigfaltigkeit ; Dimension 3 ; Topologie ; Casson-Invariante

DOI: 10.1515/9783110250367

URL: Volltext  (URL des Erstveröffentlichers)

URL: https://doi.org/10.1515/9783110250367

URL: https://www.degruyter.com/isbn/9783110250367

URL: Cover

URL: https://doi.org/10.1515/9783110250367

URL: https://www.degruyter.com/isbn/9783110250367

URL: Cover

URL: Volltext  (URL des Erstveröffentlichers)

Mehr zum Autor: Saveliev, Nikolai 1966-

UID:

Umfang: 1 online resource

Ausgabe: 2nd rev. ed.

ISBN: 3-11-025036-5

Serie: De Gruyter textbook

Inhalt: Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant. The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds.

Anmerkung: Description based upon print version of record. , Frontmatter -- , Preface / , Contents -- , Introduction -- , Glossary -- , Lecture 1. Heegaard splittings -- , Lecture 2. Dehn surgery -- , Lecture 3. Kirby calculus -- , Lecture 4. Even surgeries -- , Lecture 5. Review of 4-manifolds -- , Lecture 6. Four-manifolds with boundary -- , Lecture 7. Invariants of knots and links -- , Lecture 8. Fibered knots -- , Lecture 9. The Arf-invariant -- , Lecture 10. Rohlin's theorem -- , Lecture 11. The Rohlin invariant -- , Lecture 12. The Casson invariant -- , Lecture 13. The group SU(2) -- , Lecture 14. Representation spaces -- , Lecture 15. The local properties of representation spaces -- , Lecture 16. Casson's invariant for Heegaard splittings -- , Lecture 17. Casson's invariant for knots -- , Lecture 18. An application of the Casson invariant -- , Lecture 19. The Casson invariant of Seifert manifolds -- , Conclusion -- , Bibliography -- , Index , English

Weitere Ausg.: ISBN 3-11-025035-7

Sprache: Englisch

Fachgebiete: Mathematik

DOI: 10.1515/9783110250367

UID:

Umfang: 1 online resource (207 p.)

Ausgabe: 2nd rev. ed.

ISBN: 9783110250367 , 9783110238570

Serie: De Gruyter Textbook

Inhalt: Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant. The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds.

Anmerkung: Frontmatter -- , Preface -- , Contents -- , Introduction -- , Glossary -- , Lecture 1. Heegaard splittings -- , Lecture 2. Dehn surgery -- , Lecture 3. Kirby calculus -- , Lecture 4. Even surgeries -- , Lecture 5. Review of 4-manifolds -- , Lecture 6. Four-manifolds with boundary -- , Lecture 7. Invariants of knots and links -- , Lecture 8. Fibered knots -- , Lecture 9. The Arf-invariant -- , Lecture 10. Rohlin's theorem -- , Lecture 11. The Rohlin invariant -- , Lecture 12. The Casson invariant -- , Lecture 13. The group SU(2) -- , Lecture 14. Representation spaces -- , Lecture 15. The local properties of representation spaces -- , Lecture 16. Casson's invariant for Heegaard splittings -- , Lecture 17. Casson's invariant for knots -- , Lecture 18. An application of the Casson invariant -- , Lecture 19. The Casson invariant of Seifert manifolds -- , Conclusion -- , Bibliography -- , Index , Mode of access: Internet via World Wide Web. , In English.

In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570

In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471

In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205

In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189

In: E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233

In: E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202

Weitere Ausg.: ISBN 9783110250350

Sprache: Englisch

DOI: 10.1515/9783110250367

URL: https://doi.org/10.1515/9783110250367

URL: https://www.degruyter.com/isbn/9783110250367

URL: Cover