Intro; Supervisor's Foreword; Abstract; Acknowledgements; Contents; 1 Introduction; References; 2 Useful Mathematical Notions; 2.1 Topological Spaces; 2.2 Non-technical Definition of a Manifold; 2.3 Properties of Manifolds; 2.4 Examples of Manifolds; 2.4.1 1-Manifolds; 2.4.2 2-Manifolds; 2.4.3 3-Manifolds; 2.4.4 n-Balls and n-Spheres; 2.4.5 The Compactification of mathbbRn; 2.4.6 Product Spaces; 2.5 Defining Manifolds; 2.5.1 Hausdorff Space; 2.5.2 Bases of Topological Spaces; 2.5.3 The Rigorous Definition of a Manifold; 2.6 Homeomorphisms; 2.7 Embeddings; 2.8 The Idea of Topological Surgery

6.1 Solid 1-Dimensional Topological Surgery6.2 Solid 2-Dimensional Topological Surgery; 6.3 Modeling Phenomena Exhibiting Solid 2-Dimensional 0-Surgery; 6.4 Modeling Phenomena Exhibiting Solid 2-Dimensional 1-Surgery; References; 7 A Dynamical System Modeling Solid 2-Dimensional 0-Surgery; 7.1 The Dynamical System and Its Steady State Points; 7.2 Local Behavior and Numerical Simulations; 7.3 Connecting the Dynamical System with Solid 2-Dimensional 0-Surgery; References; 8 The Ambient Space S3; 8.1 Descriptions of S3; 8.1.1 Via mathbbR3; 8.1.2 Via Two 3-Balls; 8.1.3 Via Two Solid Tori

8.2 Connecting the Descriptions of S38.2.1 Via Corking; 8.2.2 Via Surgery; 8.3 Dynamical Systems Exhibiting the Topology of S3; 8.3.1 The 3-Dimensional Lotka-Volterra System; 8.3.2 The Pair of Linear Harmonic Oscillators; References; 9 Embedded Surgery; 9.1 Embedded 1-Dimensional Surgery; 9.2 Embedded 2-Dimensional Surgery; 9.3 Modeling Phenomena Exhibiting Embedded Solid 2-Dimensional Surgery; 9.3.1 A Topological Model for the Density Distribution in Black Hole Formation; 9.3.2 A Topological Model for the Formation of Tornadoes; 9.3.3 Embedded Solid 2-Dimensional 1-Surgery on M=D3