On the Chen character of –ideal submanifolds
Generalizing Cusick’s theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Maucourant [Mau].
The article contains a list of 7 problems related to operads and configuration spaces. Problems 1-2 are about the compactification of configuration spaces (homology and Koszulness, geometric decompositions). Problems 3-4 are about configuration spaces related to knot invariants, their geometry and Koszulness. Problems 5 to 7 are related to (operadically defined) traces and cyclic homology.
In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class...