Graduate Studies in Mathematics, Volume: 108
2009; 244 pp; hardcover
ISBN-13: 978-0-8218-4915-6
Expected publication date is December 24, 2009.
This textbook treats the classical parts of mapping degree theory, with a detailed account of its history traced back to the first half of the 18th century. After a historical first chapter, the remaining four chapters develop the mathematics. An effort is made to use only elementary methods, resulting in a self-contained presentation. Even so, the book arrives at some truly outstanding theorems: the classification of homotopy classes for spheres and the Poincare-Hopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincare, and others.
Although the mapping degree theory you will discover in this book is a classical subject, the treatment is refreshing for its simple and direct style. The straightforward exposition is accented by the appearance of several uncommon topics: tubular neighborhoods without metrics, differences between class 1 and class 2 mappings, Jordan Separation with neither compactness nor cohomology, explicit constructions of homotopy classes of spheres, and the direct computation of the Hopf invariant of the first Hopf fibration.
The book is suitable for a one-semester graduate course. There are 180 exercises and problems of different scope and difficulty.
This book is jointly published by the AMS and the Real Sociedad Matematica Espanola (RSME).
Graduate students interested in topology, particularly differential topology.
History
Manifolds
The Brouwer-Kronecker degree
Degree theory in Euclidean spaces
The Hopf Theorems
Names of mathematicians cited
Historical references
Bibliography
Symbols
Index
CBMS Regional Conference Series in Mathematics, Number: 111
2009; 110 pp; softcover
ISBN-13: 978-0-8218-4922-4
Expected publication date is December 4, 2009.
String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay between string dualities and topology and operator algebras.
The book is an interdisciplinary approach to duality symmetries in string theory. It can be read by either mathematicians or theoretical physicists, and involves a more-or-less equal mixture of algebraic topology, operator algebras, and physics. There is also a bit of algebraic geometry, especially in the last chapter. The reader is assumed to be somewhat familiar with at least one of these four subjects, but not necessarily with all or even most of them. The main objective of the book is to show how several seemingly disparate subjects are closely linked with one another, and to give readers an overview of some areas of current research, even if this means that not everything is covered systematically.
Graduate students and research mathematicians interested in mathematical physics, particularly string theory; topology; C*-algebras.
Introduction and motivation
K-theory and its relevance to physics
A few basics of C*-algebras and crossed products
Continuous-trace algebras and twisted K-theory
More on crossed products and their K-theory
The topology of T-duality and the Bunke-Schick construction
T-duality via crossed products
Higher-dimensional T-duality via topological methods
Higher-dimensional T-duality via C*-algebraic methods
Advanced topics and open problems
Bibliography
Notation and symbols
Index
American Mathematical Society Translations--Series 2, Volume: 228
2009; approx. 232 pp; hardcover
ISBN-13: 978-0-8218-4802-9
Expected publication date is January 2, 2010.
This volume contains articles on analysis, probability, partial differential operators, frames, and other areas of mathematics. The volume also contains a comprehensive article about the classification of pseudo-regular convex polyhedra.
This book is suitable for a broad group of graduate students and researchers interested in the topics presented here.
Research mathematicians interested in various areas of mathematics.
V. A. Zheludev, V. N. Malozemov, and A. B. Pevnyi -- Filter banks and frames in the discrete periodic case
A. I. Karol' -- Newton polyhedra, asymptotics of volumes, and asymptotics of exponential integrals
S. G. Kryzhevich and A. Yu. Skolyarov -- Approximation methods for unstable manifolds of equilibrium points of autonomous systems
N. G. Kuznetsov and O. V. Motygin -- The Steklov problem in symmetric domains with infinitely extended boundary
S. A. Nazarov -- On the spectrum of the Steklov problem in peak-shaped domains
V. A. Sloushch -- Generalisations of the Cwikel estimate for integral operators
A. N. Frolov -- Asymptotic behavior of probabilities of moderate deviations
A. M. Gurin and V. A. Zalgaller -- On the history of the study of convex polyhedra with regular faces and faces composed of regular ones
Contemporary Mathematics, Volume: 502
2009; 184 pp; softcover
ISBN-13: 978-0-8218-4758-9
Expected publication date is December 6, 2009.
This volume contains the proceedings of the Exploratory Workshop on Combinatorial Commutative Algebra and Computer Algebra, which took place in Mangalia, Romania on May 29-31, 2008. It includes research papers and surveys reflecting some of the current trends in the development of combinatorial commutative algebra and related fields.
This volume focuses on the presentation of the newest research results in minimal resolutions of polynomial ideals (combinatorial techniques and applications), Stanley-Reisner theory and Alexander duality, and applications of commutative algebra and of combinatorial and computational techniques in algebraic geometry and topology. Both the algebraic and combinatorial perspectives are well represented and some open problems in the above directions have been included.
Graduate students and research mathematicians interested in combinatorial commutative algebra and applications.
F. Ambro -- On the classification of toric singularities
V. Bonanzinga, V. Ene, A. Olteanu, and L. Sorrenti -- An overview on the minimal free resolutions of lexsegment ideals
V. Bonanzinga and L. Sorrenti -- Cohen-Macaulay squarefree lexsegment ideals generated in degree 2
H. Charalambous and A. Thoma -- On simple \mathcal{A}-multigraded minimal resolutions
T. C. Benitez and S. Z. Armengou -- Tangent cones of numerical semigroup rings
D. Ibadula -- The Igusa local zeta functions of GL_2(\mathbb{Q})_p-orbit of Fermat's binary form
K. Kimura, N. Terai, and K. Yoshida -- Arithmetical rank of monomial ideals of deviation two
A. D. M?cinic -- A survey of combinatorial aspects in the topology of complex hyperplane arrangements
N. Manolache -- A class of locally complete intersection multiple structures on smooth algebraic varieties as support
E. Miller -- Topological Cohen-Macaulay criteria for monomial ideals
A. Olteanu -- Regularity and the case of few generators for Stanley-Reisner ideals of subword complexes
A. tefan -- The type
Contemporary Mathematics, Volume: 503
2009; 317 pp; softcover
ISBN-13: 978-0-8218-4747-3
Expected publication date is December 18, 2009.
This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008.
These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.
Graduate students and research mathematicians interested in operator algebras and applications to dynamical systems.
J. Arnlind and S. Silvestrov -- Affine transformation crossed product type algebras and noncommutative surfaces
G. G. de Castro -- C*-algebras associated with iterated function systems
K. R. Davidson and E. G. Katsoulis -- Nonself-adjoint operator algebras for dynamical systems
S. Dirksen, M. de Jeu, and M. Wortel -- Extending representations of normed algebras in Banach spaces
T. Kajiwara -- Countable bases for Hilbert C*-modules and classification of KMS states
W. Krieger and K. Matsumoto -- Subshifts and C*-algebras from one-counter codes
K. Matsumoto -- Orbit equivalance in C*-algebras defined by actions of symbolic dynamical systems
M. McGarvey and I. G. Todorov -- Normalisers, nest algebras and tensor products
I. V. Nikolaev -- Noncommutative geometry as a functor
J. Oinert -- Simple group graded rings and maximal commutativity
H. Osaka, K. Kodaka, and T. Teruya -- The Rohlin property for inclusions of C*-algebras with a finite Watatani index
J. R. Peters -- The C*-envelope of a semicrossed product and Nest representations
N. C. Phillips -- Freeness of actions of finite groups on C*-algebras
J. Renault -- Examples of masas in C*-algebras
T. Timmermann -- A definition of compact C*-quantum groupoids
Y. Watatani -- Complex dynamical systems and associated C*-algebras
J. D. M. Wright -- On classifying monotone complete algebras of operators