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 _< I 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 4 Even surgeries 4.1 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 i nvariants from Seifert surfaces 7.5 Knots in homology spheres 7.6 Boundary links and the Alexander polynomial 7.7 Exercises 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 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 11.3 A surgery formula for the Rohlin invariant 11.4 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 l lcega~lvd splitting 16.4 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(p,q, r) 19.2 Calculation of the Casson invariant 19.3 Exercises Conclusion
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