2
votes
1answer
41 views

Recommended textbooks for Hamiltonian group actions?

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 ...
1
vote
0answers
24 views

Space of almost complex structures on a compact manifold

According to the book by Huybrechts, Complex Geometry: An Introduction, this is a nice space and may be regarded, after some form of completion, as an infinite-dimensional manifold. How is this done, ...
3
votes
1answer
109 views

Definition of Liouville measure on energy surface of Hamiltonian system

This is a reference request, as I can't for the life of me find anything that answers my question in the literature. If $(M,\omega,H)$ is a Hamiltonian system, we know from Liouvile's theorem that ...
1
vote
0answers
76 views

Sources for learning Lie groups and symplectic geometry for Quantum optics

I am asking this question on behalf of my junior who has recently joined in the graduate programme. As suggested by my boss, the student wants to work on quantum optics from a symplectic geometric ...
4
votes
2answers
295 views

Why is the moduli space of flat connections a symplectic orbifold?

In her Lectures on Symplectic Geometry on page 159, Ana Cannas da Silva writes "It turns out that $\mathcal{M}$ is a finite-dimensional symplectic orbifold." Can somebody give me a reference for ...
3
votes
0answers
109 views

Coordinate-free proof of the hamiltonian character of the geodesic flow

Let be $(M,g)$ a pseudoriemannian manifold. Let us identify the tangent and the cotangent bundles through the musical isomorphism $g^\flat:u\in TM\to g(u,\cdot)\in T^\ast M.$ It is well known ...
2
votes
0answers
138 views

How to prove that a certain action is hamiltonian?

Reading a paper I had the need to complete a proof, and come up with a certain argument(see below). My question is: could I reduce it to a special case of some theorem? I ask this question in order to ...
1
vote
1answer
147 views

References for Smale's Geometry

I read that Smale recast classical mechanics in terms of symplectic geometry. I know a bit about classical mechanics but nothing about symplectic geometry. Are there any writings from Smale on this ...