moment maps Many aspects of Hamiltonian group actions involve the moment map and not the two-form. Hence, it is often convenient to focus entirely on the properties of moment maps and to ignoreâ€¦ (More)

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of theâ€¦ (More)

We show that a small neighborhood of a closed symplectic sub-manifold in a geometrically bounded aspherical symplectic manifold has non-vanishing symplectic homology. As a consequence, we establishâ€¦ (More)

We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of theâ€¦ (More)

We show that for an even-dimensional fluid there exists a strong relation, via the Morse theory and symplectic geometry, between the topology of the vorticity function and the existence of aâ€¦ (More)

We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poissonâ€¦ (More)

In symplectic geometry, it is often useful to consider the so-called Poisson bracket on the algebra of functions on a C symplectic manifold M . The bracket determines, and is determined by, theâ€¦ (More)

The Hamiltonian flow of the standard metric Hamiltonian with respect to the twisted symplectic structure on the cotangent bundle describes the motion of a charged particle on the base. We prove thatâ€¦ (More)

Date: December 1995. Available electronically from dg-ga/9601003. The work of all three authors was partially supported by the NSF. 1 However, we will usually allow our closed two-forms to beâ€¦ (More)

Poisson Lie groups appeared in the work of Drinfel'd (see, e.g., [Drl, Dr2]) as classical objects corresponding to quantum groups. Going in the other direction, we may say that a Poisson Lie group isâ€¦ (More)