An Obstruction to the Existence of Affine Structures.
An o-minimal structure which does not admit cellular decomposition
We present an example of an o-minimal structure which does not admit cellular decomposition. To this end, we construct a function whose germ at the origin admits a representative for each integer , but no representative. A number theoretic condition on the coefficients of the Taylor series of then insures the quasianalyticity of some differential algebras induced by . The o-minimality of the structure generated by is deduced from this quasianalyticity property.
An operator invariant for handlebody-knots
A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.
An -equivariant degree and the Fuller index
An unknotting theorem for tori in 4-dimensional spheres.
Let T be a torus in S4 and T* a projection of T. If the singular set Gamma(T*) consists of one disjoint simple closed curve, then T can be moved to the standard position by an ambient isotopy of S4.
An upper estimation for the eigenfrequencies of vibrating Liapunoff bodies (first boundary value problem).
Analyse dans les topos lisses
Analysis on real affine -varieties.
Analytic and Reidemeister Torsion for Representation in Finite Type Hilbert Modules.
Analytic Foliations and the Theory of Levels.
Analytic Surgery and the Eta Invariant.
Analyticity of the free energy of a closed 3-manifold.
Analytische periodische Strömungen auf kompakten komplexen Räumen.
Andreev’s Theorem on hyperbolic polyhedra
In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that the resulting...
Anneau de cohomologie entière et -théorie d’un produit symétrique d’une surface de Riemann
Anosov Flows on New Three Manifolds.
Anosov theorem for coincidences on nilmanifolds
Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups and in their lower central series have the same dimension. We show that the Nielsen and Lefschetz coincidence numbers of maps f,g: Γ∖L → Γ’∖L’ between nilmanifolds Γ∖L and Γ’∖L’ can be computed algebraically as follows: L(f,g) = det(G⁎ - F⁎), N(f,g) = |L(f,g)|, where F⁎, G⁎ are the matrices, with respect to any preferred bases on the uniform lattices Γ and Γ’, of the homomorphisms between the Lie algebras , ’ of...
Another note on closed -cells in
Another Space-Filling Trefoil Knot.
Anti-self-dual orbifolds with cyclic quotient singularities
An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...