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Author Pereira, Jorge Vitório,
Title An invitation to web geometry / Jorge Vitorio Pereira, Luc Pirio.
Imprint Cham : Springer, [2015]

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Author Pereira, Jorge Vitório,
Series IMPA monographs ; volume 2
IMPA monographs ; volume 2.
Subject Webs (Differential geometry)
Geometry, Differential.
Alt Name Pirio, Luc,
Description 1 online resource.
polychrome rdacc
Bibliography Note Includes bibliographical references and index.
Contents Local and Global Webs -- Abelian Relations -- Abel's Addition Theorem -- The Converse to Abel's Theorem -- Algebraization -- Exceptional Webs.
Summary This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Cherns bound and Tr©♭preaus algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.
Note Vendor-supplied metadata.
ISBN 9783319145624 (electronic bk.)
3319145622 (electronic bk.)
3319145614 (print)
9783319145617 (print)
ISBN/ISSN 10.1007/978-3-319-14562-4
OCLC # 904046353
Additional Format Printed edition: 9783319145617

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