We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.
We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.
Summary: The author gives the defining relations of a new type of bialgebras that generalize both the quantum groups and braided groups as well as the quantum supergroups. The relations of the algebras are determined by a pair of matrices that solve a system of Yang-Baxter-type equations. The matrix coproduct and counit are of standard matrix form, however, the multiplication in the tensor product of the algebra is defined by virtue of the braiding map given by the matrix . Besides simple solutions...
Nous donnons des exemples de feuilletages de Lie sur une variété compacte qui ne se déforment pas en des feuilletages de Lie à holonomie discrète.