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Author: Jędrzej Śniatycki
Publisher: Cambridge University Press
ISBN: 1107022711
Category : Mathematics
Languages : en
Pages : 249
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Book Description
A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Author: Jędrzej Śniatycki
Publisher: Cambridge University Press
ISBN: 1107022711
Category : Mathematics
Languages : en
Pages : 249
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Book Description
A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Author: Jędrzej Śniatycki
Publisher:
ISBN: 9781107055599
Category : Function spaces
Languages : en
Pages : 250
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Book Description
A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Author: J. Śniatycki
Publisher: Cambridge University Press
ISBN: 1107067383
Category : Mathematics
Languages : en
Pages :
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Book Description
In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.
Author:
Publisher: Academic Press
ISBN: 9780080873244
Category : Mathematics
Languages : en
Pages : 485
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Book Description
Differential Geometry and Symmetric Spaces
Author: Joachim Schwermer
Publisher: Cambridge University Press
ISBN: 1108935079
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures and they arise in many areas of study. This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number theoretical components to the investigations of arithmetic groups, and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces, and some associated cohomological questions. Written by a renowned expert, this book is a valuable reference for researchers and graduate students.
Author: Greg Friedman
Publisher: Cambridge University Press
ISBN: 1107150744
Category : Mathematics
Languages : en
Pages : 823
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Book Description
The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.
Author: Tudor S. Ratiu
Publisher: American Mathematical Society
ISBN: 147046439X
Category : Mathematics
Languages : en
Pages : 102
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Book Description
View the abstract.
Author: Sigurdur Helgason
Publisher: American Mathematical Soc.
ISBN: 0821828487
Category : Mathematics
Languages : en
Pages : 682
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Book Description
A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
Author: N. Th. Varopoulos
Publisher: Cambridge University Press
ISBN: 1107036496
Category : Mathematics
Languages : en
Pages : 625
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Book Description
Complete account of a new classification of connected Lie groups in two classes, including open problems to motivate further study.
Author: Richard H. Cushman
Publisher: Birkhäuser
ISBN: 3034809182
Category : Science
Languages : en
Pages : 477
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Book Description
This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.
