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Moment Maps, Cobordisms, and Hamiltonian Group Actions: Mathematical Surveys and Monographs, cartea 98;

Autor Victor Guillemin, Viktor Ginzburg, Yael Karshon
en Limba Engleză Hardback – 21 noi 2002
This research monograph presents many new results in a rapidly developing area of great current 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 exciting new research. During the last 20 years, ``localization'' has been one of the dominant themes in the area ofequivariant 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 allconsequences 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 propergroup-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 theoreticalphysicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
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Specificații

ISBN-13: 9780821805022
ISBN-10: 0821805029
Pagini: 350
Dimensiuni: 187 x 256 x 22 mm
Greutate: 0.82 kg
Editura: American Mathematical Society
Colecția American Mathematical Society
Seria Mathematical Surveys and Monographs

Locul publicării:Oxford, United States