Fibrations à la Ganea

Towards mirror symmetry à la SYZ for generalized Calabi–Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal sixmanifold M with static SU(2) structure and mirror M̂ , it is argued that the product M×M̂ is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and M̂ . The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric an...

Simplicial Resolutions and Ganea Fibrations

In this work, we compare the two approximations of a pathconnected space X, by the Ganea spaces Gn(X) and by the realizations ‖Λ•X‖n of the truncated simplicial resolutions emerging from the loop-suspension cotriple ΣΩ. For a simply connected space X, we construct maps ‖Λ•X‖n−1 → Gn(X) → ‖Λ•X‖n over X, up to homotopy. In the case n = 2, we prove the existence of a map G2(X) → ‖Λ•X‖1 over X (up ...

L'universite Du Quebec a Chicoutimi Comme Exigence Partielle De La Maitrise En Informatique Offerte À L'université Du Quebec À Chicoutimi Par

Hyperplane Arrangements and Milnor Fibrations

— There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the h...

Science Education in France: ‘la Main À La Pâte’