I am doing a project on Hamiltonian group actions on symplectic manifolds, and my supervisor was able to list several good books on Riemannian geometry to start me off, but he didn't know of any single place to learn about Hamiltonian groups.

I have found some books (even available online from the author!) that come highly recommended, specifically: Introduction to Symplectic and Hamiltonian Geometry, A. C. da Silva.

As the title suggests however, this seems to come from more of a geometric standpoint. Which books are recommended that might focus on the group-theory and topology end of this subject? The project description specifically mentions cohomological obstructions, something that I think is related to group cohomology? (At this point I'm getting all of this from Wikipedia...)

I have had basic, introductory courses in Differential Geometry (in $\mathbb{R}^n$) and in topology (up to calculating the first fundamental group of a topological space).

Thank you in advance for any input!


Hamiltonian group actions are fundamentally geometric, since the definition involves the symplectic structure on a manifold. Any good treatment will certainly pay attention to the topological, aspects, but I don't know quite what you mean for the group-theoretic aspects. I find Lie group theory to be more a field of geometry than algebra. I would recommend McDuff-Salamon's Symplectic Topology as well, with the caveat that neither book is easy.

That said, I'm also happy to share my notes from lectures by Andreas Ott, which explain some details which da Silva and McDuff are likely to assume.


The project is now finished, and for anybody else looking to do something similar, I would like to add the following book as an excellent source for an introduction to the material:

An Introduction to Symplectic Geometry, Berndt

This was found more helpful than any of the others, (save perhaps da Silva's lectures) as a short-term introduction to the subject.


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