| Preface | p. xiii |
| Introduction | p. 1 |
| Acknowledgments | p. 9 |
| A Fast Trip Through the Classical Theory | |
| An example: The Pham-Brieskorn polynomials | p. 11 |
| The local conical structure | p. 14 |
| Ehresmann's fibration lemma | p. 17 |
| Milnor's fibration theorem for real singularities | p. 18 |
| Open book decompositions and fibred knots | p. 21 |
| On Milnor's fibration theorem for complex singularities | p. 22 |
| The join of Pham and the topology of the Milnor fibre. The Milnor number | p. 25 |
| Exotic spheres and the topology of the link | p. 30 |
| Motions in Plane Geometry and the 3-dimensional Brieskorn Manifolds | |
| Groups of motions in the 2-sphere. The polyhedral groups | p. 36 |
| Triangle groups and the classical plane geometries | p. 42 |
| The 3-sphere as a Lie group and its finite subgroups | p. 47 |
| Brieskorn manifolds and Klein's theorem | p. 50 |
| The group PSL(2, R) and its universal cover SL(2, R) | p. 55 |
| Milnor's theorem for the 3-dimensional Brieskorn manifolds. The hyperbolic case | p. 57 |
| Brieskorn-Hamm complete intersections. The theorem of Neumann | p. 60 |
| Remarks | p. 62 |
| 3-dimensional Lie Groups and Surface Singularities | |
| Quasi-Homogeneous surface singularities | p. 65 |
| 3-manifolds whose universal covering is a Lie group | p. 71 |
| Lie groups and singularities I: quasi-homogeneous singularities | p. 75 |
| Lie groups and singularities II: the cusps | p. 80 |
| Lie groups and singularities III: the Abelian and E[superscript +] (2)-cases | p. 82 |
| A uniform picture of 3-dimensional Lie groups | p. 85 |
| Lie algebras and the Gorenstein property | p. 87 |
| Remarks | p. 88 |
| Within the Realm of the General Index Theorem | |
| A review of characteristic classes | p. 92 |
| On Hirzebruch's theorems about the signature and Riemann-Roch | p. 97 |
| Spin and Spin[superscript c] structures on 4-manifolds. Rochlin's theorem | p. 102 |
| Spin and Spin[superscript c] structures on complex surfaces. Rochlin's theorem | p. 105 |
| A review of surface singularities | p. 110 |
| Gorenstein and numerically Gorenstein singularities | p. 116 |
| An application of Riemann-Roch: Laufer's formula | p. 121 |
| Geometric genus, spin[superscript c] structures and characteristic divisors | p. 126 |
| On the signature of smoothings of surface singularities | p. 128 |
| On the Rochlin [mu] invariant for links of surface singularities | p. 131 |
| Comments on new 3-manifolds invariants and surface singularities | p. 134 |
| On the Geometry and Topology of Quadrics in CP[superscript n] | |
| The topology of a quadric in CP[superscript n] | p. 138 |
| The space CP[superscript n] as a double mapping cylinder | p. 141 |
| The orthogonal group SO(n + 1,R) and the geometry of CP[superscript n] | p. 143 |
| Cohomogeneity 1-actions of SO(3) on CP[superscript 2] and S[superscript 4] | p. 148 |
| The Arnold-Kuiper-Massey theorem | p. 150 |
| Real Singularities and Complex Geometry | |
| The space of Siegel leaves of a linear flow | p. 157 |
| Real singularities and the Lopez de Medrano-Verjovsky-Meersseman manifolds | p. 163 |
| Real singularities and holomorphic vector fields | p. 167 |
| On the topology of certain real hypersurface singularities | p. 170 |
| Real Singularities with a Milnor Fibration | |
| Milnor's fibration theorem revisited | p. 175 |
| The strong Milnor condition | p. 177 |
| Real singularities of the Pham-Brieskorn type | p. 181 |
| Twisted Pham-Brieskorn singularities and the strong Milnor condition | p. 187 |
| On the topology of the twisted Pham-Brieskorn singularities | p. 191 |
| Stability of the Milnor conditions under perturbations | p. 194 |
| Remarks and open problems | p. 196 |
| Real Singularities and Open Book Decompositions of the 3-sphere | |
| On the resolution of embedded complex plane curves | p. 200 |
| The resolution and Seifert graphs | p. 204 |
| Seifert links and horizontal fibrations | p. 206 |
| An example | p. 209 |
| Resolution and topology of the singularities z[superscript p subscript 1]z[subscript 2] + z[superscript q subscript 2]z[subscript 1] = 0 | p. 213 |
| On singularities of the form fg | p. 216 |
| Bibliography | p. 221 |
| Index | p. 235 |
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