A corrigendum to the paper “Connecting direct limit topologies with metrics on infinite-dimensional manifolds”
A countable dense homogeneous space with a dense rigid open subspace
We show that there is a Polish space which is countable dense homogeneous but contains a dense open rigid connected subset. This answers several questions of Fitzpatrick and Zhou.
A Counterexample to a Conjecture of Steenrod.
A criterion for homeomorphism between closed Haken manifolds.
A criterion for the noncellularity of arcs
A curious remark concerning the geometric transfer map.
A decomposition into homeomorphic handlebodies with naturally equivalent involutions.
A decomposition theorem for h-cobordant smooth simply-connected compact 4-manifolds.
A Deformation Lemma on a C1 manifold.
A description based on Schubert classes of cohomology of flag manifolds
We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.
A description of Chern classes of semistable sheaves on a quadric surface.
A dynamical approach to compactify the three dimensional Lorentz group.
A Euclidean geometric invariant of framed (Un)Knots in manifolds.
A factorization lemma and its application to realization of mappings as inverse limits
A faithful linear-categorical action of the mapping class group of a surface with boundary
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin-structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.
A family of flat Minkowski planes admitting 3-dimensional simple groups of automorphisms.
A Family of Impossible Figures Studied by Knot Theory
A Fatou-Julia decomposition of transversally holomorphic foliations
A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Saludes. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when discussing...
A few remarks about symplectic filling.
A few remarks on the geometry of the space of leaf closures of a Riemannian foliation
The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space. In Section...