Singularities and Topology of Hypersurfaces

Alexandru Dimca9780387977096, 0387977090, 3540977090

This book systematically presents a large number of basic results on the topology of complex algebraic varieties using the information on the local topology and geometry of a singularity. These concepts are then used in the computation of global topological invariants, such as homology groups, cohomology groups, fundamental groups, and Alexander polynomials. The reader will derive from this text a working knowledge of Whitney stratifications, Lefschetz-type theorems, knots and links, Milnor fibrations, vanishing cycles, weighted projective space, mixed Hodge structures and many other related notions and results. The book is intended for graduate work in algebraic and differential topology, and is an excellent source of natural examples and open-ended problems for the student working on a dissertation.