Topics on Real and Complex Singularities

Abstract

The fourth Japanese-Australian Workshop on Real and Complex Singularities (JARCS4 KOBE 2011) was held at the Kobe Satellite of Hyogo University of Teacher Education during the period 22-25 November, 2011. There were 31 participants from Australia and Japan. The Australian and Japanese Singularity groups have built up strong research relationship in the past three decades. For instance, the blow-analytic theory introduced by Tzee-Char Kuo in Australia has been intensively developed in Japan. In addition, a lot of joint research works of both countries have been established in several topics related to real and complex singularities. The present volume mainly consists of the texts of the invited talks of the workshop. Some of them are joint works of Australians and Japanese. This volume contains original articles on real and complex singularities, topology of differentiable maps, openings of differentiable map-germs, the relationship between free divisors and holonomic systems, effective computation method of invariants of singularities, the application of singularity theory to differential geometry, the deformation theory of CR structures and differential equation with singular points. In these articles some new notions important for characterizations of singularities are introduced, and several new results are presented. New approaches to classical topics and new computation methods of singularities are also presented.