04941nam a22005895i 4500 978-3-031-52481-3 DE-He213 20251030112259.0 cr nn 008mamaa 240605s2024 sz | s |||| 0|eng d 9783031524813 978-3-031-52481-3 10.1007/978-3-031-52481-3 doi QA564-609 PBMW bicssc MAT012010 bisacsh PBMW thema Handbook of Geometry and Topology of Singularities V: Foliations [electronic resource] / edited by Felipe Cano, José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XXVI, 510 p. 73 illus., 29 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 1 Bruno Scárdua, Holomorphic foliations: singularities and local geometric aspects -- 2 Yu. Ilyashenko, Persistence, uniformizanion and holonomy -- 3 Laura Ortiz-Bobadilla, Ernesto Rosales-González and Sergei Voronin, Holomorphic foliations and vector fields with degenerated singularity in (C2, 0) -- 4 David Marín, Jean-Francois Mattei and Eliane Salem, Topology of singular foliation germs in C2 -- 5 Nuria Corral, Jacobian and polar curves of singular foliations -- 6 Dmitry Novikov and Sergei Yakovenko, Rolle models in the Real and Complex world -- 7 Fernando Sanz Sánchez, Half a century with the problem of the gradient of an analytic function -- 8 Jose Manuel Aroca, Newton Polygon -- 9 Jorge Vitório Pereira, Closed meromorphic 1-forms. This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. This Volume V focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering: The fibers of a smooth map between differentiable manifolds, with singularities at the critical points. The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy. The kernel of appropriate 1-forms. The singularities are the zeros of the form. Open books, which naturally appear in singularity theory as foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory. This volume, like its companion Volume VI, also focused on foliations, consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. The volume starts with a foreword by one of the current world leaders in the theory of complex foliations. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook. Algebraic geometry. Geometry, Differential. 69684 Topological groups. 72299 Lie groups. 72300 Functions of complex variables. 72222 Algebraic Geometry. Differential Geometry. 69686 Topological Groups and Lie Groups. 72304 Several Complex Variables and Analytic Spaces. 72225 Cano, Felipe. editor. edt http://id.loc.gov/vocabulary/relators/edt 78302 Cisneros-Molina, José Luis. editor. edt http://id.loc.gov/vocabulary/relators/edt 78303 Dũng Tráng, Lê. editor. edt http://id.loc.gov/vocabulary/relators/edt 78304 Seade, José. editor. edt http://id.loc.gov/vocabulary/relators/edt 78305 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031524806 Printed edition: 9783031524820 Printed edition: 9783031524837 https://doi.org/10.1007/978-3-031-52481-3 ZDB-2-SMA ZDB-2-SXMS 60534 60534