Mathematical Surveys and Monographs, Volume: 166
2010; approx. 411 pp; hardcover
ISBN-13: 978-0-8218-5231-6
Expected publication date is October 29, 2010.
Seifert fiberings extend the notion of fiber bundle mappings by allowing some of the fibers to be singular. Away from the singular fibers, the fibering is an ordinary bundle with fiber a fixed homogeneous space. The singular fibers are quotients of this homogeneous space by distinguished groups of homeomorphisms. These fiberings are ubiquitous and important in mathematics. This book describes in a unified way their structure, how they arise, and how they are classified and used in applications. Manifolds possessing such fiber structures are discussed and range from the classical three-dimensional Seifert manifolds to higher dimensional analogues encompassing, for example, flat manifolds, infra-nil-manifolds, space forms, and their moduli spaces. The necessary tools not covered in basic graduate courses are treated in considerable detail. These include transformation groups, cohomology of groups, and needed Lie theory. Inclusion of the Bieberbach theorems, existence, uniqueness, and rigidity of Seifert fiberings, aspherical manifolds, symmetric spaces, toral rank of spherical space forms, equivariant cohomology, polynomial structures on solv-manifolds, fixed point theory, and other examples, exercises and applications attest to the breadth of these fiberings. This is the first time the scattered literature on singular fiberings is brought together in a unified approach. The new methods and tools employed should be valuable to researchers and students interested in geometry and topology.
Graduate students and research mathematicians interested in topology (transformation groups. manifolds, singular fiberings, and differential geometry).
Introduction
Transformation groups
Group actions and the fundamental group
Actions of compact Lie groups on manifolds
Definition of Seifert fibering
Group cohomology
Lie groups
Seifert fiber space construction for Gtimes W
Generalization of Bieberbach's theorems
Seifert manifolds with Gammasetminus G/K-fiber
Locally injective Seifert fiberings with torus fibers
Applications
Seifert fiberings with compact connected Q
Deformation spaces
S^1-actions on 3-dimensional manifolds
Classification of Seifert 3-manifolds via equivariant cohomology
Bibliography
Index
Contemporary Mathematics, Volume: 522
2010; 206 pp; softcover
ISBN-13: 978-0-8218-4750-3
Expected publication date is October 7, 2010.
This volume contains a collection of papers from the Conference on Vector Bundles held at Miraflores de la Sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday.
The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, Hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.
Graduate students and research mathematicians interested in vector bundles on algebraic varieties and related topics.
Contemporary Mathematics,Volume: 523
2010; 244 pp; softcover
ISBN-13: 978-0-8218-4956-9
Expected publication date is October 3, 2010.
This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, ON, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007.
The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0,1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes.
Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interest and of benefit both to the experienced and to newcomers alike.
Graduate students and research mathematicians interested in information theory, finite geometries, codes, or cryptography.
Cryptography
C. J. Colbourn and J. Torres-Jimenez -- Heterogeneous hash families and covering arrays
W. J. Martin and B. Sunar -- Resilient functions: Just how resilient are they?
M. Mosca and D. Stebila -- Quantum coins
J. R. Oldford and D. L. Wehlau -- Optimal block lengths for secret key distillation
Finite geometries
T. L. Alderson -- Hyperconics and multiple weight codes for OCDMA
A. A. Bruen -- Blocking sets and large transversal-free systems of mutually orthogonal Latin squares
A. A. Bruen, T. C. Bruen, and R. Silverman -- Incidence matrices with forbidden configurations
M. Iurlo and S. Rajola -- A new method to construct maximal partial spreads of smallest size in PG(3,q)
M. S. Tallini -- A representation of the projective space P(r,k) on the affine plane A(2,k) and the geometric equivalence between the Veblen configuration in P(3,k) and the Desargues configuration in A(2,k)
J. A. Thas and H. Van Maldeghem -- Andre embeddings of affine planes
Codes
A. Barg and P. Purkayastha -- Near MDS poset codes and distributions
J. Bierbrauer, D. Bartoli, S. Marcugini, and F. Pambianco -- Geometric constructions of quantum codes
A. Bogatyrev, M. Hassner, and D. Yarmolich -- An exact analytical-expression for the read sensor signal in magnetic data storage channels
A. A. Bruen -- Blocking sets and low-weight codewords in the generalized Reed-Muller codes
V. C. Gaudet -- Low-power LDPC decoding by exploiting the fault-tolerance of the sum-product algorithm
O. Heden -- On perfect codes over non prime power alphabets
M. Lavrauw, L. Storme, and G. Van de Voorde -- Linear codes from projective spaces
T. P. McDonough and V. C. Mavron -- The dimension of the code of a strongly resolvable design
G. E. Moorhouse -- Codes of nets and projective planes
C. Schlegel -- Minimum output symbol error variance of forward error control codes
D. Truhachev and M. Rahbari -- Multi-stream information transmission in random power attenuation environments
ISBN-13: 9780805382914
About the Book
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text’s usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. Students will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. The style and treatment of topics is now more consistent across chapters.
The Second Edition has been updated for currency and consistency across all topics and has been checked for the right amount of mathematical rigor.
The chapter on scattering theory (Chapter 6 in this edition) is completely reorganized, with a new introduction based on time dependent perturbation theory.
Explicit solutions to the Schrodinger Wave Equation have been added, including the linear potential, the simple harmonic oscillator using generating functions, and the derivation of spherical harmonics.
A discussion of SO(4) symmetry and its application to solving the hydrogen atom and approximation techniques based on extreme time dependences have been added to early chapters.
The chapter on identical particles (Chapter 7 in this edition) is now expanded to include the technique of second quantization and its application to electrons in solids and the quantized electromagnetic field.
A new chapter on relativistic wave mechanics has been added (Chapter 8).
Discussion, including literature references, of experimental demonstration of quantum mechanical phenomena is featured, including: the Stern-Gerlach experiment on cesium atoms, muon spin rotation and g-2, neutrino oscillations, “bouncing” ultracold neutrons, Berry's phase with neutrons, elastic scattering of protons from nuclei, the effects of exchange symmetry in nuclear decay, and the Casimir effect, among others.
Advanced mathematical techniques (for example generating functions and contour integrals) associated with quantum mechanical calculations appear throughout.
Paperback (ISBN-13: 9780521127073)
Page extent: 232 pages
Size: 234 x 156 mm
Preface; Notation and special symbols; Historical introduction; 1. Plane Euclidean geometry; 2. Affine transformations in the Euclidean plane; 3. Finite groups of isometries of E2; 4. Geometry on the sphere; 5. The projective plane P2; 6. Distance geometry on P2; 7. The hyperbolic plane; Appendices; References; Index.