Moment Maps, Cobordisms and Hamiltonian Group Actions Hardback
by Victor Guillemin, Viktor Ginzburg, Yael Karshon
Part of the Mathematical Surveys and Monographs series
Hardback
Description
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 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.
Information
-
Item not Available
- Format:Hardback
- Pages:350 pages, bibliography; index
- Publisher:American Mathematical Society
- Publication Date:01/09/2002
- Category:
- ISBN:9780821805022
Other Formats
- PDF from £86.40
Information
-
Item not Available
- Format:Hardback
- Pages:350 pages, bibliography; index
- Publisher:American Mathematical Society
- Publication Date:01/09/2002
- Category:
- ISBN:9780821805022
