curves and singularities a geometrical introduction to singularity theory

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Curves And Singularities

Author : James William Bruce
ISBN : 0521429994
Genre : Mathematics
File Size : 82. 97 MB
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The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors take a novel approach by casting the theory into a new light, that of singularity theory. The second edition of this successful textbook has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added that covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to the modern theories of catastrophes and singularities.

Real And Complex Singularities

Author : Ana Claudia Nabarro
ISBN : 9781470422059
Genre : Differential geometry -- Classical differential geometry -- Classical differential geometry
File Size : 64. 13 MB
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This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)

Singular Points Of Plane Curves

Author : C. T. C. Wall
ISBN : 0521547741
Genre : Mathematics
File Size : 37. 84 MB
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Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.

Singularities In Geometry And Topology

Author : Jean-Paul Brasselet
ISBN : 9789812700223
Genre : Mathematics
File Size : 46. 77 MB
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Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Singularities Of Smooth Functions And Maps

Author : J. Martinet
ISBN : 0521233984
Genre : Mathematics
File Size : 65. 49 MB
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Introduction To Singularities And Deformations

Author : Gert-Martin Greuel
ISBN : 9783540284192
Genre : Mathematics
File Size : 30. 55 MB
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Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Singularities In Geometry And Topology

Author :
ISBN : 9789814477048
Genre :
File Size : 51. 65 MB
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Algebraic Geometry And Singularities

Author : Antonio Campillo Lopez
ISBN : 9783034890205
Genre : Mathematics
File Size : 57. 10 MB
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Singularity Theory

Author : Charles Terence Clegg Wall
ISBN : 0521658888
Genre : Computers
File Size : 46. 55 MB
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An up-to-date survey of research in singularity theory.

Ebene Algebraische Kurven

Author : Egbert Brieskorn
ISBN : UOM:39015049066551
Genre : Mathematics
File Size : 60. 23 MB
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