Singularity theory encompasses many different aspects of geometry and topology, and an overview of these is represented here by papers given at the International Singularity Conference held in 1991 at Lille. The conference attracted researchers from a wide variety of subject areas, including differential and algebraic geometry, topology, and mathematical physics. Some of the best known figures in their fields participated, and their papers have been collected here. Contributors to this volume include G. Barthel, J.W. Bruce, F. Delgado, M. Ferrarotti, G.M. Greuel, J.P. Henry, L. Kaup, B....

This volume collects papers presented at the eighth Sao Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.

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Vector?eldsonmanifoldsplaymajorrolesinmathematicsandothersciences. In particular, the Poincar e Hopf index theorem and its geometric count- part, the Gauss Bonnettheorem, giveriseto the theoryof Chernclasses, key invariants of manifolds in geometry and topology. One has often to face problems where the underlying space is no more a manifold but a singular variety. Thus it is natural to ask what is the good notionofindexofavector?eld, andofChernclasses, ifthespaceacquiress- gularities.Thequestionwasexploredbyseveralauthorswithvariousanswers, starting with the pioneering work of M.-H. Schwartz...

Singularity theory appears in numerous branches of mathematics, as well as in many other areas such as robotics, control theory, imaging, and various areas in physics. This book covers the developments in singularity theory and intends to introduce young researchers from developing countries to singularities in geometry and topology.

This volume constitutes the Proceedings of the Fourth Franco-Japanese Symposium on Singularities held at Toyama in August 2007 and also the Workshop on Singularities held at Niigata prior to this Symposium. Recently the research on singularities is widely expanding and is now applied in various areas in Mathematics and other sciences. Experts of singularities from many different fields are contributing their articles, mostly on original results and some surveys. The reader will benefit of knowing the vividly developing domains and will be inspired by many different approaches to...