Analytic Cycles of Finite Type

Daniel Barlet studied mathematics at the ENS Ulm (Paris) from 1966 to 1970. After his graduation he became assistant professor at the University of Paris VII, where he defended his these d'etat in December 1974. From 1976 to 2011 he was professor at the University of Nancy I, which is today a part of the University of Lorraine. He was president of the French Mathematical Society (92/94) and was elected as a senior member of the Institut Universitaire de France (Complex Analysis and Complex Geometry) from 1998 to 2003. His chair was renewed for a further five years in 2003. Since 2011 he has been professor emeritus at the Institute of Elie Cartan at the University of Lorraine. Jón Ingólfur Magnússon obtained a B.Sc. in mathematics at the University of Iceland in 1976 and a doctoral degree in mathematics from the University of Paris VII (Jussieu) in 1981. Since then, he has been working, first as a research mathematician and later as a professor, at the University of Iceland. In 2023 he became a professor emeritus at the University of Iceland. His research interests are mainly in cycle space theory.    The authors wrote a two volume work on analytic cycles in complex spaces which was published by the French Mathematical Society (Cours Spécialisés 22 and 27) in 2014 and 2020. An improved English version of the first volume was published by Springer (Grundlehren der mathematischen Wissenschaften 356) in 2019 and an English version of the second volume will soon be published in the same series.

• Chapter 1. Semi-proper maps.- Chapter 2. Quasi-proper Maps.- Chapter 3. The space Cfn (M).- Chapter 4. f-Analytic Families of Cycles.- Chapter 5. Geometrically f-Flat Maps and Strongly Quasi-proper Maps.- Chapter 6. Applications.