AbstractThe topological group of homeomorphisms of d-dimensional Euclidean space is a basic object in geometric topology, closely related to understanding the difference between diffeomorphisms and homeomorphisms of all d-dimensional manifolds (except when d=4). I will explain some methods that have been used for studying the algebraic topology of this group, and report on a recently obtained c...
AbstractThe knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier, or to use its geodesic distance to measure similarity between points. Classical problems for manifold learning are often posed in a very high dimension, e.g...