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Hamiltonian Group Actions and Equivariant Cohomology (Paperback, 1st ed. 2019)
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Hamiltonian Group Actions and Equivariant Cohomology (Paperback, 1st ed. 2019)
Series: SpringerBriefs in Mathematics
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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.
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