A general Fredholm theory I: a splicing-based differential geometry
A Note on the Alexander Theorem on the Complex Plane
We investigate the Banach manifold consisting of complex functions on the unit disc having boundary values in a given one-dimensional submanifold of the plane. We show that ∂/∂λ̅ restricted to that submanifold is a Fredholm mapping. Moreover, for any such function we obtain a relation between its homotopy class and the Fredholm index.
Euler-Poincaré index theory on Banach manifolds
Examples of infinite dimensional isoparametric submanifolds.
Fredholm spectrum and growth of cohomology groups
Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let be the non-essential spectrum of T. We show that, for each connected component M of the manifold of all smooth points of , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups grow at least like the sequence with d = dim M.
Global geometric aspects of Riemann-Hilbert problems.
Gluing complex discs to Lagrangian manifolds by Gromov’s method
The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.
Homotopy classes of elliptic transmission problems over -algebras.
L-homology theory of FSQL-manifolds and the degree of FSQL-mappings
A homology theory of Banach manifolds of a special form, called FSQL-manifolds, is developed, and also a homological degree of FSQL-mappings between FSQL-manifolds is introduced.
Nonlinear structures determined by measures on Banach spaces
On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications.
On injective holomorphic Fredholm mappings of index 0 in complex Banach spaces
Plateau's Problem for surfaces of constant mean curvature form a global point of view.
Remarks on the solvability and nonsolvability of weakly nonlinear equations
Riemannian structures and -homology. (Structures riemanniennes et -homologie.)
Some Theorems on Direct Limits of Expanding Sequences of Manifolds.
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 geometry of Kato Grassmannians
We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.
The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds
In this paper we study Lipschitz-Fredholm vector fields on bounded Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if is a connected smooth bounded Fréchet-Finsler manifold endowed with a connection and if is a smooth Lipschitz-Fredholm vector field on with respect to which satisfies condition (WCV), then, for any smooth functional on which is associated to , the set of the critical values of is of first category in . Therefore,...
Théorie du degré dans certains espaces de Fréchet d'après R. S. Hamilton