On the Fundamental Group of a Visibility Manifold.
For and a link map let , define a map by and a (generalized) Massey-Rolfsen invariant to be the homotopy class of . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps up to link concordance to . If are closed highly homologically connected manifolds of dimension (in particular, homology spheres), then .
In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.
In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.
The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.