Younes, Laurent

Invariance, deformations et reconnaissance de formes

Series: Mathematiques et Applications , Vol. 44

2004, XVII, 248 p., Softcover
ISBN: 3-540-40868-1
Due: October 22, 2003

About this textbook

Cet ouvrage introduit un certain nombre de techniques disponibles pour la reconnaissance de formes planes, en mettant l'accent sur l'importance de la prise en compte des deux notions essentielles que sont l'invariance et l'analyse des deformations. En conciliant autant qu'il se peut les aspects theoriques fondamentaux et les techniques algorithmiques realistes, il revisite les differentes methodes de representation de formes, allant des representations parametriques invariantes aux axes medians, decrit, sous un eclairage original un certain nombre de techniques de detection de formes, et developpe des resultats recents sur l'analyse des deformations et la mise en correspondance de formes et d'images. Il est susceptible de servir a la fois de reference pour le chercheur que d'ouvrage d'introduction a la theorie pour l'etudiant de troisieme cycle.

Table of contents

Avant-propos.- Partie I: Varietes, Groupes de Lie et Invariance; Elements de Geometrie differentielles; Invariants.- Partie II: Representation de formes planes; Representations parametriques; Representations implicites; Axe median; Representation par des moments; Representations relatives a un prototype.- Partie III: Les formes dans les images; Contour actifs; Analyse statistique d'indices concordants.- Partie IV: Analyse de deformations; Groupes de diffeommorphismes; Estimation de diffeomorphismes; Distances et action de groupe.- Literature.- Index.

Pilgrim, Kevin M.

Combinations of Complex Dynamical Systems

Series: Lecture Notes in Mathematics , Vol. 1827

2003, IX, 118 p., Softcover
ISBN: 3-540-20173-4

About this book

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.

Written for: Researchers and graduate students in complex dynamical systems and low-dimensional topology

Keywords: Complex dynamics, postcritically finite

Table of contents

Introduction.- Preliminaries.- Combinations.- Uniqueness of combinations.- Decompositions.- Uniqueness of decompositions.- Counting classes of annulus maps.- Applications to mapping class groups. Examples.- Canonical decomposition theorem.

Berline, Nicole, Getzler, Ezra, Vergne, Michele

Heat Kernels and Dirac Operators

Series: Grundlehren Text Editions

2004, X, 362 p., Softcover
ISBN: 3-540-20062-2
Due: November 1, 2003

About this textbook

In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback. The first four chapters could be used as the text for a graduate course on the applications of linear elliptic operators in differential geometry and the only prerequisites are a familiarity with basic differential geometry. The next four chapters discuss the equivariant index theorem, and include a useful introduction to equivariant differential forms. The last two chapters give a proof, in the spirit of the book, of Bismut's Local Family Index Theorem for Dirac operators.

Written for: Graduate students and researchers in differential geometry, Arakelov geometry, group representation theory and mathematical physics

Table of contents

Introduction.- Background on Differential Geometry.- Asymptotic Expansion of the Heat Kernel.- Clifford Modules and Dirac Operators.- Index Density of Dirac Operators.- The Exponential Map and the Index Density.- The Equivariant Index Theorem.- Equivariant Differential Forms.- The Kirillov Formula for the Equivariant Index.- The Index Bundle.- The Family Index Theorem.- Bibliography.- List of Notations.- Index.

Akivis, Maks, Goldberg, Vladislav

Differential Geometry of Varieties with Degenerate Gauss Maps

Series: CMS Books in Mathematics

2004, Approx. 235 p. 16 illus., Hardcover
ISBN: 0-387-40463-5
Due: November 1, 2003

About this textbook

In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps. The authors introduce the above mentioned methods and apply them to a series of concrete problems arising in the theory of varieties with degenerate Gauss maps. What makes this book unique is the authors? use of a systematic application of methods of projective differential geometry along with methods of the classical algebraic geometry for studying varieties with degenerate Gauss maps. This book is intended for researchers and graduate students interested in projective differential geometry and algebraic geometry and their applications. It can be used as a text for advanced undergraduate and graduate students. Each author has published over 100 papers and they have each written a number of books, including Conformal Differential Geometry and Its Generalizations (Wiley 1996), Projective Differential Geometry of Submanifolds (North-Holland 1993), and Introductory Linear Algebra (Prentice-Hall 1972), which were written by them jointly.

Written for: 2nd year graduate students, mathematics researchers

Table of contents

Preface.- Foundational Material.- Varieties in Projective Spaces and Their Gauss Maps.- Basic Equations of Varieties with Degenerate Gauss Maps.- Main Structure Theorems.- Further Examples and Applications of the Theory of Varieties with Degenerate Gauss Maps.- Bibliography.- Symbols Frequently Used.- Author Index.- Subject Index.

Godement, Roger

Introduction a la theorie des groupes de Lie

2004, IX, 305 pp., Softcover
ISBN: 3-540-20034-7
Due: November 24, 2003

About this book

Ces notes de cours donnes il y a une trentaine d'annees a Paris mais restees d'actualite couvrent la theorie generale des groupes de Lie, ainsi que quelques points de la theorie des groupes topologiques, groupes discontinus notamment. Le cas des groupes lineaires, expose avant la theorie generale par la methode de von Neumann, permet d'expliquer plus naturellement le formalisme de celle-ci. Ce livre pourra aussi completer les volumes III (3-540-66142-5) et IV (43841-6) de l'Analyse Mathematique du meme auteur.

Written for: Etudiants de licence et de ma?rise, enseignants universitaires en cours d'analyse, enseignants en classes pracaratoires

Keywords: Groupes de Lie, groupes lineaires, groupes localement compacts, groupes discrets