Algebraic Fiber Bundles

Contact Fiber Bundles

We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are construction of K-contact manifolds generalizing Yamazaki’s fiber join construction and a cross-section theorem for contact moment maps.

Locally definable fiber bundles

Let η = (E, p, Y, F, K) be a locally definable fiber bundle and f, h : X → Y two locally definable maps. If f and h are locally definably homotopic, then f ∗(η) and h∗(η) are locally definably fiber bundle isomorphic. 2000 Mathematics Subject Classification. 14P10, 14P20, 03C64.

Vector bundles over algebraic curves

Illustrative White Matter Fiber Bundles

Diffusion Tensor Imaging (DTI) has made feasible the visualization of the fibrous structure of the brain white matter. In the last decades, several fiber-tracking methods have been developed to reconstruct the fiber tracts from DTI data. Usually these fiber tracts are shown individually based on some selection criteria like region of interest. However, if the white matter as a whole is being vi...

Symplectic structures on fiber bundles

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 symplectomorphisms. In this paper, building on prior...