| Description |
1 online resource (ix, 199 pages) : illustrations |
| Series |
De Gruyter textbook |
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De Gruyter textbook.
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| Contents |
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 â?? 1 -- 1.6 Seifert Manifolds -- 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 -- 3 Kirby Calculus -- 3.1 The Linking Number -- 3.2 Kirby Moves -- 3.3 The Linking Matrix |
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3.4 Reversing Orientation 4 Even Surgeries -- 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 -- 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 -- 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 |
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7.5 Knots In Homology Spheres 7.6 Boundary Links And The Alexander Polynomial -- 8 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 -- 9 The Arf-Invariant -- 9.1 The Arf-Invariant Of A Quadratic Form -- 9.2 The Arf-Invariant Of A Knot -- 10 Rohlinâ€?S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of QÌ? -- 10.3 Representing Homology Classes By Surfaces -- 11 The Rohlin Invariant |
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11.1 Definition Of The Rohlin Invariant 11.2 The Rohlin Invariant Of Seifert Spheres -- 11.3 A Surgery Formula For The Rohlin Invariant -- 11.4 The Homology Cobordism Group -- 12 The Casson Invariant -- 13 The Group Su(2) -- 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 Of Seifert Homology Spheres -- 15 The Local Properties Of Representation Spaces |
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16 Casson�S Invariant For Heegaard Splittings 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 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 Unlinks -- 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 -- 19 The Casson Invariant Of Seifert Manifolds |
| Summary |
"Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."--Jacket |
| Bibliography |
Includes bibliographical references (pages 186-195) and index |
| Notes |
Print version record |
| Subject |
Three-manifolds (Topology)
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MATHEMATICS -- Topology.
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Three-manifolds (Topology)
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Casson-Invariante
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Mannigfaltigkeit
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Dimension 3
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Topologie
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| Form |
Electronic book
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| LC no. |
99040959 |
| ISBN |
9783110806359 |
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3110806355 |
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