الصفحة 1
الصفحة 1
On the Topology of Isolated Singularities in Analytic Spaces
The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry.
Conformal Groups in Geometry and Spin Structures
This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley and progressing to recent research in spinors and conformal geometry. Key topics and features: * Focuses initially on the basics of Clifford algebras * Studies the spaces of spinors for some even Clifford algebras * Examines conformal spin geometry, beginning with an elementary study of the conformal group of the Euclidean plane * Treats covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the complex conformal group * Introduces conformal flat geometry and conformal spinoriality groups, followed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure * Discusses links between classical spin structures and conformal spin structures in the context of conformal connections * Examines pseudo-unitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associated with the classical pseudo-unitary space
