05157nam a22005895i 4500 978-3-031-54172-8 DE-He213 20251030112321.0 cr nn 008mamaa 240620s2024 sz | s |||| 0|eng d 9783031541728 978-3-031-54172-8 10.1007/978-3-031-54172-8 doi QA564-609 PBMW bicssc MAT012010 bisacsh PBMW thema Handbook of Geometry and Topology of Singularities VI: Foliations [electronic resource] / edited by Felipe Cano, José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XXII, 487 p. 8 illus., 6 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 1 Adolfo Guillot, On the singularities of complete holomorphic vector fields in dimension two -- 2 Julio Rebelo and Helena Reis, Singularities of holomorphic vector fields in dimensions ≥ 3: results and problems -- 3 Alcides Lins Neto, Codimension one holomorphic Foliations -- 4 Maurıcio Correa, Analytic varieties invariant by holomorphic foliations and Pfaff systems -- 5 Felipe Cano and Beatriz Molina-Samper, Local Invariant Hypersurfaces for Singular Foliations -- 6 Isao Nakai, From the perspective of nonsolvable dynamics on (C, 0): Basics and Applications -- 7 Javier Ribon, Description of the Zariski-closure of a group of formal diffeomorphisms -- 8 Frank Loray, The Riemann-Hilbert correspondence for rank 2 meromorphic connections on curves -- 9 Emmanuel Paul, Jean-Pierre Ramis, Dynamics of the fifth Painlevé foliation -- 10 Jean-Pierre Ramis, Epilogue: Stokes phenomena. Dynamics, Classification Problems and Avatars. This is the sixth 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 VI goes together with Volume V and 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 zeroes of the form. Open books, which naturally appear in singularity theory, are foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory. This volume 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. Volume VI ends with an Epilogue by one of the current world leaders in the theory of complex foliations, with plenty of open questions and ideas for further research. 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: 9783031541711 Printed edition: 9783031541735 Printed edition: 9783031541742 https://doi.org/10.1007/978-3-031-54172-8 ZDB-2-SMA ZDB-2-SXMS 60861 60861