On the Topology of Isolated Singularities in Analytic Spaces

Author: José Seade

Publisher: Springer Science & Business Media

ISBN: 3764373954

Category: Mathematics

Page: 238

View: 7502

The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.


Author: Daniel Bättig,Horst Knörrer

Publisher: Springer-Verlag

ISBN: 3034886578

Category: Mathematics

Page: 140

View: 5353

Resolution of Singularities

A research textbook in tribute to Oscar Zariski Based on the courses given at the Working Week in Obergurgl, Austria, September 7–14, 1997

Author: Herwig Hauser,Joseph Lipman,Frans Oort,Adolfo Quirós

Publisher: Springer Science & Business Media

ISBN: 9783764361785

Category: Mathematics

Page: 598

View: 4994

In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

Birational Geometry of Algebraic Varieties

Author: Janos Kollár,Shigefumi Mori

Publisher: Cambridge University Press

ISBN: 9780521060226

Category: Mathematics

Page: 254

View: 9388

This book provides the first comprehensive introduction to the circle of ideas developed around Mori's program.

Jahresbericht der Deutschen Mathematiker-Vereinigung

Jubiläumstagung 100 Jahre DMV, Bremen 1990 : Hauptvorträge

Author: Wulf-Dieter Geyer,Deutsche Mathematiker-Vereinigung

Publisher: N.A


Category: Mathematics

Page: 348

View: 8305

Stable Solution of Inverse Problems

Author: Johann Baumeister

Publisher: Vieweg + Teubner Verlag


Category: Language Arts & Disciplines

Page: 254

View: 5117

These notes are intended to describe the basic concepts of solving inverse problems in a stable way. Since almost all in­ verse problems are ill-posed in its original formulation the discussion of methods to overcome difficulties which result from this fact is the main subject of this book. Over the past fifteen years, the number of publications on inverse problems has grown rapidly. Therefore, these notes can be neither a comprehensive introduction nor a complete mono­ graph on the topics considered; it is designed to provide the main ideas and methods. Throughout, we have not striven for the most general statement, but the clearest one which would cover the most situations. The presentation is intended to be accessible to students whose mathematical background includes basic courses in ad­ vanced calculus, linear algebra and functional analysis. Each chapter contains bibliographical comments. At the end of Chap­ ter 1 references are given which refer to topics which are not studied in this book. I am very grateful to Mrs. B. Brodt for typing and to W. Scondo and u. Schuch for inspecting the manuscript.

Kürschners deutscher Gelehrten-Kalender

Author: Gerhard Lüdtke,Katrin Hofmann,Hans Strodel,Hans Jaeger

Publisher: Berlin

ISBN: 9783598236037

Category: Scholars

Page: 1456

View: 8907


Author: Gerhard Lüdtke,K. G. Saur Verlag GmbH & Company,Kurschners Deutscher Gelehrten-Kalender,Hans Strodel,K. g. Saur,Hans Jaeger

Publisher: N.A

ISBN: 9783598236297

Category: German literature

Page: 5239

View: 8366

Each volume includes "Wissenschaftliche zeitschriften."

Regular Solids and Isolated Singularities

Author: Klaus Lamotke

Publisher: Vieweg+Teubner Verlag

ISBN: 9783528089580

Category: Mathematics

Page: 224

View: 1541

The last book XIII of Euclid's Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl~fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the finite rotation groups. He introduced complex coordinates and by means of invariant theory associated polynomial equations with these groups. These equations in turn describe isolated singularities of complex surfaces. The structure of the singularities is investigated by methods of commutative algebra, algebraic and complex analytic geometry, differential and algebraic topology. A paper by DuVal from 1934 (see the References), in which resolutions play an important rele, marked an early stage of these investigations. Around 1970 Klein's polynomials were again related to new mathematical ideas: V. I. Arnold established a hierarchy of critical points of functions in several variables according to growing com plexity. In this hierarchy Kleinls polynomials describe the "simple" critical points.