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| 1 Homology 3-Spheres 1.1 Integral Homology 3-Spheres 1.1.1 Homotopy 3-Spheres 1.1.2 Poincare Homology Sphere 1.1.3 Brieskorn Homology Spheres 1.1.4 Seifert Fibered Homology Spheres 1.1.5 Dehn Surgery on Knots 1.1.6 Surgery on Links 1.1.7 Connected Sums and Splicing 1.1.8 Splice Decomposition 1.1.9 Plumbing 1.1.10 Links of Singularities 1.1.11 Mutations 1.1.12 Branched Covers 1.1.13 Heegaard Splittings of Homology Spheres. 1.2 Rational Homology Spheres 1.2.1 Spherical Space Forms 1.2.2 Dehn Surgery 1.2.3 Seifert Fibered Manifolds 1.2.4 Links of Singularities 1.2.5 Branched Covers 2 Rokhlin Invariant. 2.1 The Rokhlin Theorem 2.2 Definition of the Rokhlin Invariant 2.3 Properties of the Rokhlin Invariant 2.3.1 Surgery Formula for the Rokhlin Invariant 2.3.2 Surgery on Algebraically Split Links 2.3.3 Splicing and Mutation 2.3.4 Rokhlin Invariant of Branched Coverings 2.3.5 Birman-Craggs Homomorphisms 2.3.6 Homology Cobordism Invariance 2.4 Seifert Fibered and Graph Homology Spheres 2.4.1 The Algorithm 2.4.2 The Formula 3 Casson Invariant 3.1 Definition of the Casson Invariant 3.2 Construction of the Casson Invariant 3.2.1 SU(2)-Representation Spaces 3.2.2 The Intersection Theory 3.2.3 Orientations 3.2.4 Independence of Heegaard Splitting 3.2.5 Casson Invariant for Knots and Property (1) 3.2.6 The Difference Cycle 3.2.7 Casson Invariant for Boundary Links and Property (2) 3.2.8 Casson Invariant of a Trefoil and Property (0) 3.3 Comments and Ramifications 3.3.1 Pillowcase 3.3.2 Perturbations 3.3.3 The Connected Sum Formula 3.3.4 The Integrality of A(Z) 3.3.5 Casson Invariant of Algebraically Split Links 3.4 Properties of the Casson Invariant 3.4.1 Splicing Additivity 3.4.2 Mutation Invariance 3.4.3 Casson Invariant of Branched Coverings 3.4.4 Casson Invariant of Fibered Knots 3.4.5 Finite Type Invariants 3.4.6 Further Properties of the Casson Invariant 3.5 Seifert Fibered and Graph Homology Spheres 3.5.1 Casson Invariant of 3.5.2 Casson Invariant of 3.5.3 The Neumann-Wahl Conjecture 3.6 Applications of the Casson Invariant 3.6.1 Triangulating Topological 4-Manifolds 3.6.2 Amphicheiral Homology Spheres 3.6.3 Property P for Knots 4 Invariants of Walker and Lescop 4.1 Definition of the Walker Invariant 4.2 Construction of the Walker Invariant 4.2.1 SU(2)-Representation Varieties 4.2.2 The Intersection Theory 4.2.3 The Surgery Formula 4.2.4 Combinatorial Definition of the Walker Invariant 4.3 The Lescop Invariant 4.4 Properties of the Walker and Lescop Invariants 4.4.1 The Gluing Formula 4.4.2 Branched Covers 4.4.3 Seifert Fibered Manifolds 4.5 Casson Type Invariants from Other Lie Groups 5 Casson Invariant adn Gauge Theory 6 Instanton Floer Homeology 7 The Homology Cobordism Group References Index |
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