September 2003 | Hardback | 183 pages 30
line diagrams | ISBN:
0-521-83197-0
This book gives a quick introduction to the
theory of foliations,
Lie groupoids and Lie algebroids. An important
feature is the
emphasis on the interplay between these concepts:
Lie groupoids
form an indispensable tool to study the transverse
structure of
foliations as well as their noncommutative
geometry, while the
theory of foliations has immediate applications
to the Lie theory
of groupoids and their infinitesimal algebroids.
The book starts
with a detailed presentation of the main
classical theorems in
the theory of foliations then proceeds to
Molino's theory, Lie
groupoids, constructing the holonomy groupoid
of a foliation and
finally Lie algebroids. Among other things,
the authors discuss
to what extent Lieｿs theory for Lie groups
and Lie algebras
holds in the more general context of groupoids
and algebroids.
Based on the authorsｿ extensive teaching
experience, this book
contains numerous examples and exercises
making it ideal for
graduate students and their instructors.
Contents
1. Foliations; 2. Holonomy and stability;
3. Two classical
theorems; 4. Molinoｿs theory; 5. Lie groupoids;
6. Lie
algebroids.
September 2003 | Paperback | 300 pages |
ISBN: 0-88385-811-8
The International Mathematical Olympiad competition
is held every
year with the final taking place in a different
country. The
final consists of a two day exam with the
contestants being
challenged to solve three difficult problems
each day. This book
contains the questions from the finals taking
place between 1986
and 1999 inclusive. For each problem the
author has included at
least one solution and often remarks about
alternative approaches
and the significance of the problem. Many
of the solutions are
derived from answers given by contestants
rather than the
organisers as these were often the most elegant
solutions. This
collection will be of great value to students
preparing for the
IMO and to all others who are interested
in problem solving in
mathematics.
Contents
1. Problems; 2. Solutions.
September 2003 | Paperback | 200 pages |
ISBN: 0-521-52999-9
Most integrable systems owe their origin
to problems in geometry
and they are best understood in a geometrical
context. This is
especially true today when the heroic days
of KdV-type
integrability are over. Problems that can
be solved using the
inverse scattering transformation have reached
the point of
diminishing returns. Two major techniques
have emerged for
dealing with multi-dimensional integrable
systems: twistor theory
and the d-bar method, both of which form
the subject of this book.
It is intended to be an introduction, though
by no means an
elementary one, to current research on integrable
systems in the
framework of differential geometry and algebraic
geometry. This
book arose from a seminar, held at the Feza
Gursey Institute, to
introduce advanced graduate students to this
area of research.
The articles are all written by leading researchers
and are
designed to introduce the reader to contemporary
research topics.
Contributors
L. Mason, K. P. Tod, N. M. J. Woodhouse,
R. Y. Donagi, P.
Santini, F. Calogero, Y. Nutku
Contents
1. Introduction Lionel Mason; 2. Differential
equations featuring
many periodic solutions F. Calogero; 3. Geometry
and
integrability R. Y. Donagi; 4. The anti self-dual
Yang-Mills
equations and their reductions Lionel Mason;
5. Curvature and
integrability for Bianchi-type IX metrics
K. P. Tod; 6. Twistor
theory for integrable equations N. M. J.
Woodhouse; 7. Nonlinear
equations and the d-bar problem P. Santini.
October 2003 | Hardback | 904 pages 140 line
diagrams 30 half-tones
5 tables | ISBN: 0-521-82081-2
Based on lectures given in honour of Stephen
Hawkingｿs sixtieth
birthday, this book comprises contributions
from some of the
worldｿs leading theoretical physicists. It
begins with a
section containing chapters by successful
scientific
popularisers, bringing to life both Hawkingｿs
work and other
exciting developments in physics. The book
then goes on to
provide a critical evaluation of advanced
subjects in modern
cosmology and theoretical physics. Topics
covered include the
origin of the universe, warped spacetime,
cosmological
singularities, quantum gravity, black holes,
string theory,
quantum cosmology and inflation. As well
as providing a
fascinating overview of the wide variety
of subject areas to
which Stephen Hawking has contributed, this
book represents an
important assessment of prospects for the
future of fundamental
physics and cosmology.
Contributors
Martin J. Rees, Jame B. Hartle, Roger Penrose,
Kip Thorne,
Stephen W. Hawking, George F. R. Ellis, Matt
Visser, Brandon
Carter, Roger Penrose, Werner Israel, Martin
J. Rees, Bernard
Carr, Simon F. Ross, Steven Giddings, Malcolm
Perry, Joe
Polchinski, Gary Horowitz, Leonard Susskind,
Gary Gibbons, Ian
Moss, Chris Isham, Abhay Ashtekar, Fay Dowker,
Edward Witten,
David Gross, Michael Green, Paul Townsend,
Nick Warner, Chris
Pope, Raphael Bousso, Andrew Strominger,
Renata Kallosh, James B.
Hartle, Don Page, A. Vilenkin, Bryce de Witt,
J. Halliwell, Peter
DｿEath, Alan Guth, Paul Shellard, Neil Turok,
Andrei Linde,
Pierre Binetruy
2003 Approx. 470 p. Hardcover
3-7643-2189-X
Assuming that the reader is familiar with
sheaf theory, the book gives a self-contained
introduction to the theory of constructible
sheaves related to many kinds of singular
spaces, such as cell complexes, triangulated
spaces, semialgebraic and subanalytic sets,
complex algebraic or analytic sets, stratified
spaces, and quotient spaces. The relation
to the underlying geometrical ideas are worked
out in detail, together with many applications
to the topology of such spaces. All chapters
have their own detailed introduction, containing
the main results and definitions, illustrated
in simple terms by a number of examples.
The technical details of the proof are postponed
to later sections, since these are not needed
for the applications.
Keywords: Algabraic topology, Sheaves, Singular
spaces, Monodromy, Algebraic geometry, Category
theory, Triangulation, Localization, Morse
theory
Contents:
Introduction.- 1. Thom-Sebastiani Theorem
for Constructible Sheaves.- 2. Constructible
Sheaves in Geometric Categories.- 3. Localization
Results for Equivariant Constructible Sheaves.-
4. Stratification Theory and Constructible
Sheaves.- 5. Morse Theory for Constructible
Sheaves.- 6. Vanishing Theorems for Constructible
Sheaves.- Bibliography.- Index.
Series: Monografie Matematyczne. Vol.. 63