Learn More
Studies in experimental animals and humans have stressed the role of the cerebellum in motor skill learning. Yet, the relative importance of the cerebellar cortex and deep nuclei, as well as the nature of the dynamic functional changes occurring between these and other motor-related structures during learning, remains in dispute. Using functional magnetic(More)
We study in this paper the rational homotopy type of the space of symplectic embeddings of the standard ball B 4 (c) ⊂ R 4 into 4-dimensional rational symplectic manifolds. We compute the rational homotopy groups of that space when the 4-manifold has the form M λ = (S 2 × S 2 , µω 0 ⊕ ω 0) where ω 0 is the area form on the sphere with total area 1 and µ(More)
Let G be a connected subgroup of the group Diff(M) of diffeomorphisms of a manifold M. It is well known that every element φ ∈ π 1 (G, id) defines an endomorphism ∂ φ : H * (M, Q) → H * +1 (M, Q) as follows. Choose a loop {φ t }, t ∈ S 1 , of diffeomorphisms from G representing φ and a cycle C in M. Then the homology class ∂ φ ([C]) is represented by the(More)
Let π : P → B be a locally trivial fiber bundle over a connected CW complex B with fiber equal to the closed symplectic manifold (M, ω). Then π is said to be a symplectic fiber bundle if its structural group is the group of symplectomorphisms Symp(M, ω), and is called Hamiltonian if this group may be reduced to the group Ham(M, ω) of Hamiltonian(More)
The " Flux conjecture " for symplectic manifolds states that the group of Hamiltonian diffeomorphisms is C 1-closed in the group of all symplectic dif-feomorphisms. We prove the conjecture for spherically rational manifolds and for those whose minimal Chern number on 2-spheres either vanishes or is large enough. We also confirm a natural version of the Flux(More)