A Polish AR-Space with no Nontrivial Isotopy
The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.
A proof of Reidemeister-Singer’s theorem by Cerf’s methods
Heegaard splittings and Heegaard diagrams of a closed 3-manifold are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
Bi-Lipschitz Concordance Implies Bi-Lipschitz Isotopy.
Decomposition spaces having arbitrarily small neighborhoods with 2-sphere boundaries II
Geometric topology of stratified spaces.
Homeomorphisms of the sphere and a generalization of the Whyburn conjecture for compact connected manifolds with boundary
Local subhomeotopy groups of bounded surfaces.
On pseudo-isotopy classes of homeomorphisms of a dimensional differentiable manifold.
We study self-homotopy equivalences and diffeomorphisms of the (n+1)-dimensional manifold X= #p(S1 x Sn) for any n ≥ 3. Then we completely determine the group of pseudo-isotopy classes of homeomorphisms of X and extend to dimension n well-known theorems due to F. Laudenbach and V. Poenaru (1972,1973), and J. M. Montesinos (1979).
On the relative Schoenflies theorem.
Quelques remarques sur les diagrammes de Heegard
Subexponential groups in 4-manifold topology.
Tightness and efficiency of irreducible automorphisms of handlebodies.
Topological properties of high-dimensional handles