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The Workshop on Real and Complex Singularities is held every other year at the Instituto de Ciencias Matematicas e de Computacao (Sao Carlos, Brazil) and brings together specialists in the vanguard of singularities and its applications. This volume contains articles contributed by participants of the seventh workshop.

The main subjects of the Siegen Topology Symposium are reflected in this collection of 16 research and expository papers. They center around differential topology and, more specifically, around linking phenomena in 3, 4 and higher dimensions, tangent fields, immersions and other vector bundle morphisms. Manifold categories, K-theory and group actions are also discussed.

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Any topological theory of knots and links should be based on simple ideas of intersection and linking. In this book, a general theory of link bordism in manifolds and universal constructions of linking numbers in oriented 3-manifolds are developed. In this way, classical concepts of link theory in the 3-spheres are generalized to a certain class of oriented 3-manifolds (submanifolds of rational homology 3-spheres). The techniques needed are described in the book but basic knowledge in topology and algebra is assumed. The book should be of interst to those working in topology, in particular knot theory and low-dimensional topology.

The purpose of this book is to , particularly those associated with the calculus of variations, in a modern geometric way.