Expected publication date is December 6,
2003
Description
Rolfsen's beautiful book on knots and links
can be read by
anyone, from beginner to expert, who wants
to learn about knot
theory. Beginners find an inviting introduction
to the elements
of topology, emphasizing the tools needed
for understanding
knots, the fundamental group and van Kampen's
theorem, for
example, which are then applied to concrete
problems, such as
computing knot groups. For experts, Rolfsen
explains advanced
topics, such as the connections between knot
theory and surgery
and how they are useful to understanding
three-manifolds.
Besides providing a guide to understanding
knot theory, the book
offers "practical" training. After
reading it, you will
be able to do many things: compute presentations
of knot groups,
Alexander polynomials, and other invariants;
perform surgery on
three-manifolds; and visualize knots and
their complements. It is
characterized by its hands-on approach and
emphasis on a visual,
geometric understanding.
Rolfsen offers invaluable insight and strikes
a perfect balance
between giving technical details and offering
informal
explanations. The illustrations are superb,
and a wealth of
examples are included.
Now back in print by the AMS, the book is
still a standard
reference in knot theory. It is written in
a remarkable style
that makes it useful for both beginners and
researchers.
Particularly noteworthy is the table of knots
and links at the
end. This volume is an excellent introduction
to the topic and is
suitable as a textbook for a course in knot
theory or 3-manifolds.
Contents
Introduction
Codimension and other matters
The fundamental group
Three-dimensional pl geometry
Seifert surfaces
Finite cyclic coverings and the torsion invariants
Infinite cyclic coverings and the Alexander
invariant
Matrix invariants
3-manifolds and surgery on links
Foliations, branched covers, fibrations and
so on
A higher-dimensional sampler
Covering spaces and some algebra in a nutshell
Dehn's lemma and the loop theorem
Table of knots and links
References
Index
Details:
Series: AMS Chelsea Publishing
Publication Year: 2003
ISBN: 0-8218-3436-3
Paging: 439 pp.
Binding: Hardcover
Description
In the decade since the discovery that Artin's
braid groups enjoy
a left-invariant linear ordering, several
quite different
approaches have been applied to understand
this phenomenon. This
book is an account of those approaches, involving
self-distributive
algebra, uniform finite trees, combinatorial
group theory,
mapping class groups, laminations, and hyperbolic
geometry.
This volume is suitable for graduate students
and research
mathematicians interested in algebra and
topology.
Contents
A linear ordering of braids
Self-distributivity
Handle reduction
Finite trees
Automorphisms of a free group
Curve diagrams
Hyperbolic geometry
Triangulations
Bi-ordering the pure braid groups
Open questions
Bibliography
Index
Index of notation
Details:
Series: Panoramas et Syntheses, Number: 14
Publication Year: 2002
ISBN: 2-85629-135-X
Paging: 190 pp.
Binding: Softcover
Publication Date Sep 2003
Length 312pp,
ISBN Hardback:0-7503-0959-8
Contents
Preface (A Kundu) A Journey Through the KdV
Equation (M
Lakshmanan) The Painleve methods (R Conte
and M Musette) Discrete
Integrability (K M Tamizhmani, A Ramani,
B Grammaticos and T
Tamizhmani) The D-BAR Method: A Tool for
Solving Two-Dimensional
Integrable Evolution PDEs (A S Fokas) Introduction
to Solvable
Lattice Models in Statistical and Mathematical
Physics (T Deguchi)II.
QUANTUM SYSTEMS Unifying Approaches in Integrable
Systems:
Quantum and Statistical, Ultralocal and Nonultralocal
(A Kundu)
The Physical Basis of Integrable Spin Models
(I Bose) Exact
Solvability in Contemporary Physics (A Foerster,
J Links and H-Q
Zhou) The Thermodynamics of the spin-1/2
XXX Chain: Free Energy
and Low-temperature Singularities of Correlation
Lengths (A KlEper
and C Scheeren) Reaction-Diffusion Processes
and Their Connection
with Integrable Quantum Spin Chains (M Henkel)
Synopsis
Nonlinear integrable systems, covering both
classical and quantum
models, are of considerable theoretical and
practical interest,
with applications over a wide range of subjects
from water waves
to spin models, nonlinear optics to correlated
electron systems,
plasma physics to reaction-diffusion processes.
Classical and Quantum Nonlinear Integrable
Systems reviews the
advances made in various facets of this subject.
Emphasis is
placed on the underlying concepts rather
than technicalities and
it is intended to serve as an introduction
to the subject for
those interested in the field as well as
being useful to
specialists. The book divides into two parts,
the first covering
classical theories and applications, the
second devoted to the
quantum aspects of the subject.
Readership
Advanced graduate students and researchers
in mathematical
physics and applied mathematics
Publication Date Dec 2003
Length c400pp, illus
ISBN Paperback:0-7503-0950-4
Contents
Part V Non-Abelian Symmetries Part VI Quantum
Chromodynamics (QCD)
Part VII Spontaneous Symmetry Breaking Part
VII Weak Interactions
and the Electroweak Theory
Full Text Contents
Synopsis
Gauge Theories in Particle Physics Volume
1: From Relativistic
Quantum Mechanics to QED discussed the formulation
and
application of quantum electrodynamics, which
is now regarded as
simply the first part of the standard model
of particle physics.
In Gauge Theories in Particle Physics Volume
2: QCD and the
Electroweak Theory the remaining two parts
of the standard model,
namely, quantum chromodynamics and the electroweak
theory of
Glashow, Salam and Weinberg are considered.
These latter two
theories are in some ways like QED but there
are important
differences, which create significant conceptual
and technical
difficulties for the student. The aim of
the book is to ease the
reader through these difficulties, keeping
the level of
accessibility comparable to that of volume
1, and thus provide a
much more accessible introduction to these
theories than is
available elsewhere. As was also the case
in volume 1,
substantial attention is paid to calculations
of physical
quantities, and to comparison of the resulting
predictions with
experimental results.
The similarities between QED and the two
theories studied in
volume 2 include the facts that all three
are gauge theories,
that the calculation methods of Feynman graphs
can be applied to
all of them, and that they are all renormalizable.
So the
foundations of gauge theory, Feynman graphs
and renormalization
theory laid in volume 1 continue to be highly
relevant in volume
2. Nevertheless, there are important differences
between QED and
the other two theories.
Readership
Graduate and senior undergraduate students
taking courses on the
standard model of particle physics. Postgraduate
students and
researchers in particle physics
ISBN: 0-471-46068-0
Paperback
240 pages
July 2003
Author Information
A guide to choosing and using the right techniques
High-speed computers and prepackaged statistical
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