The Hilbert modular group, resolution of the singularities at the cusps and related problems
The Hochschild cohomology of a closed manifold
Let M be a closed orientable manifold of dimension dand be the usual cochain algebra on M with coefficients in a fieldk. The Hochschild cohomology of M, is a graded commutative and associative algebra. The augmentation map induces a morphism of algebras . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of , which is in general quite small. The algebra is expected to be isomorphic...
The *-holonomy group of the Stefan suspension of a diffeomorphism
The definition of a Stefan suspension of a diffeomorphism is given. If is the Stefan suspension of the diffeomorphism g over a Stefan foliation , and G₀ ∈ satisfies the condition , then we compute the *-holonomy group for the leaf determined by G₀. A representative element of the *-holonomy along the standard imbedding of S¹ into F₀ is characterized. A corollary for the case when G₀ contains only one point is derived.
The Homology of Cyclic and Irregular Dihedral Coverings Branched Over Homology Spheres.
The homology of some groups of diffeomorphisms.
The Hörmander and Maslov classes and Fomenko's conjecture.
The Identity Component of the Leaf Preserving Diffeomorphism Group is Perfect.
The index of analytic vector fields and Newton polyhedra
We prove that if f:(ℝⁿ,0) → (ℝⁿ,0) is an analytic map germ such that and f satisfies a certain non-degeneracy condition with respect to a Newton polyhedron Γ₊ ⊆ ℝⁿ, then the index of f only depends on the principal parts of f with respect to the compact faces of Γ₊. In particular, we obtain a known result on the index of semi-weighted-homogeneous map germs. We also discuss non-degenerate vector fields in the sense of Khovanskiĭand special applications of our results to planar analytic vector fields....
The index of discontinuous vector fields.
The index of signature operators on Lipschitz manifolds
The integral cohomology rings of real infinite-dimensional flag manifolds
The Intersection Matrix of Brieskorn Singularities.
The Irregularities of Hirzebruch's Examples of Surfaces of General Type with c21= 3c2 .
The Kervaire invariant of immersions.
The Kevaire Invariant of Hypersurfaces in Complex Projective Spaces.
The L²-invariants and Morse numbers
We study the homotopy invariants of free cochain complexes and Hilbert complexes. These invariants are applied to calculation of exact values of Morse numbers of smooth manifolds.
The Lie affine foliations on 4-manifolds.
The link of an extrovert divide
The linking number of singular maps.
The Lyusternik-Shnirel'man category, vector bundles, and immersions of manifolds.