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.
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.
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.
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.
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