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Author: William Norrie Everitt
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 94
ISBN-13: 0821835459
DOWNLOAD EBOOKComplex symplectic spaces are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. This title presents a self-contained investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality.
Author: William Norrie Everitt
Publisher:
Published: 2004
Total Pages: 76
ISBN-13: 9781470404116
DOWNLOAD EBOOKComplex symplectic spaces are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. This title presents a self-contained investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality.
Author: Alan Huckleberry
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 385
ISBN-13: 3034882270
DOWNLOAD EBOOKInfinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.
Author: Ana Cannas da Silva
Publisher: Springer
Published: 2004-10-27
Total Pages: 240
ISBN-13: 354045330X
DOWNLOAD EBOOKThe goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author: P.R. Chernoff
Publisher: Springer
Published: 2006-11-15
Total Pages: 165
ISBN-13: 3540372873
DOWNLOAD EBOOKAuthor: Boris Khesin
Publisher: Springer Science & Business Media
Published: 2008-09-28
Total Pages: 304
ISBN-13: 3540772634
DOWNLOAD EBOOKThis monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Author: Irving Ezra Segal
Publisher:
Published: 1966
Total Pages: 26
ISBN-13:
DOWNLOAD EBOOKAuthor: Kiyoshi Igusa
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 114
ISBN-13: 0821837737
DOWNLOAD EBOOKIntends to prove that higher Franz-Reidemeister (FR) torsion satisfies the transfer property and a formula known as the 'Framing Principle' in full generality. This title uses these properties to compute the higher FR-torsion for various smooth bundles with oriented closed even dimensional manifold fibers.
Author: Leon Armenovich Takhtadzhi︠a︡n
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 136
ISBN-13: 0821839365
DOWNLOAD EBOOKIn this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).
Author: Nicholas Michael John Woodhouse
Publisher: Oxford University Press
Published: 1992
Total Pages: 324
ISBN-13: 9780198502708
DOWNLOAD EBOOKThe geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
