Micro-Bundles with Infinite-Dimensional Fibers are Trivial.
On infinite-dimensional manifolds
On the homotopical classification of DJ-mappings of infnitely dimensional spheres
On the structure of Hilbert cube manifolds
On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.
Periodic actions on (I-D) normed linear spaces
Periodic actions on the Hilbert cube
Property Z and Property Y sets in F-manifolds
Pseudo-interiors of hyperspaces
Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum
We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space .
Some Topological Properties of Kähler Manifolds and Homogeneous Spaces.
Stable Classification of Infinite-Dimensional Manifolds by Homotopy-Type.
Sur la topologie de l’espace des opérateurs pseudodifférentiels inversibles d’ordre 0
Les groupes d’homotopie du groupe (stabilisé) des opérateurs pseudodifférentiels inversibles d’ordre zéro agissant sur une variété compacte sans bord sont calculés en termes de la -théorie du fibré cosphérique . Du même coup, on montre que le sous-groupe des perturbations compactes inversibles de l’identité est faiblement rétractile dans . Les résultats sont aussi adaptés au cas des opérateurs suspendus. Des applications à la théorie de l’indice et pour le déterminant résiduel de Simon Scott...
The Canonical Class and the Properties of Kähler Surfaces.
The closure of the space of homeomorphisms on a manifold. The piecewise linear case
The density problem for infinite dimensional group actions
Théorie du degré dans certains espaces de Fréchet d'après R. S. Hamilton
Topological groups and convex sets homeomorphic to non-separable Hilbert spaces
Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f n: X → X)nεgw such that each f n is -near to the identity map of X and the family f n(X)n∈ω is locally finite...
Vector fields on the Sato Grassmannian.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.
Гомотопии пространств диффеоморфизмов некоторых трехмерных многообразий