Moment Maps, Cobordisms, and Hamiltonian Group Actions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Moment Maps, Cobordisms, and Hamiltonian Group Actions write by Victor Guillemin. This book was released on 2002. Moment Maps, Cobordisms, and Hamiltonian Group Actions available in PDF, EPUB and Kindle. During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
Moment Maps, Cobordisms, and Hamiltonian Group Actions
Moment Maps, Cobordisms, and Hamiltonian Group Actions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Moment Maps, Cobordisms, and Hamiltonian Group Actions write by Victor Guillemin. This book was released on 2002. Moment Maps, Cobordisms, and Hamiltonian Group Actions available in PDF, EPUB and Kindle. This research monograph presents results in a rapidly developing area of great contemporary interest. Guillemin, Ginzburg, and Karshon show that the underlying topological thread in the computation of invariants of G-manifolds is a consequence of a linearization theorem involving equivariant cobordisms. The book incorporates a novel approach and showcases progressive research. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an abstract moment map'.
Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces
Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces write by Victor Guillemin. This book was released on 2012-10-08. Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces available in PDF, EPUB and Kindle. The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. This book is addressed to researchers and can be used as a semester text.
Hamiltonian Group Actions and Equivariant Cohomology
Hamiltonian Group Actions and Equivariant Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hamiltonian Group Actions and Equivariant Cohomology write by Shubham Dwivedi. This book was released on 2019-09-23. Hamiltonian Group Actions and Equivariant Cohomology available in PDF, EPUB and Kindle. This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.
Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications
Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications write by Stephen Wiggins. This book was released on . Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications available in PDF, EPUB and Kindle. This monograph, which grew out of a series of lectures delivered by Stephen Wiggins at the Fields Institute in early 1993, is concerned with the geometrical viewpoint of the global dynamics of nonlinear dynamical systems. With appropriate examples and concise explanations, Wiggins unites many different topics into one volume and makes a unique contribution to the field. Engineers, physicists, chemists, and mathematicians who work on issues related to the global dynamics of nonlinear dynamical systems will find these lectures very useful.
