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.
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. 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.
Equivariant Cohomology and Localization of Path Integrals
Equivariant Cohomology and Localization of Path Integrals - 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 Equivariant Cohomology and Localization of Path Integrals write by Richard J. Szabo. This book was released on 2003-07-01. Equivariant Cohomology and Localization of Path Integrals available in PDF, EPUB and Kindle. This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.
Convexity Properties of Hamiltonian Group Actions
Convexity Properties of 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 Convexity Properties of Hamiltonian Group Actions write by Victor Guillemin. This book was released on 2005. Convexity Properties of Hamiltonian Group Actions available in PDF, EPUB and Kindle. This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic" case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel su This volume is recommended for independent study and is suitable for graduate students and researchers interested in symplectic geometry, algebraic geometry, and geometric combinatorics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.
Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology
Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology - 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 Torus Actions in Equivariant Cohomology and Symplectic Topology write by Milena Dorota Pabiniak. This book was released on 2012. Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology available in PDF, EPUB and Kindle. The central theme of this work are Hamiltonian torus actions on symplectic manifolds. We investigate the invariants of the action, and use the action to answer questions about the invariants of the manifold itself.
