Related papers: p-Adic Heisenberg Cantor sets, 3

Using elementary counting methods of weight systems for finite type invariants of knots and integral homology 3-spheres, in the spirit of [B-NG], we answer positively three questions raised in [Ga]. In particular, we exhibit a one-to-one…

We introduce Smale-Vietoris diffeomorphisms that include the classical DE-mappings with Smale solenoids. We describe the correspondence between basic sets of axiom A Smale-Vietoris diffeomorphisms and basic sets of nonsingular axiom A…

Explicit solutions for the three-term recurrence satisfied by associated continuous dual $q$-Hahn polynomials are obtained. A minimal solution is identified and an explicit expression for the related continued fraction is derived. The…

We explain how to construct certain potential functions for the hyperbolic structures of a knot complement, which are closely related to the analytic functions on the deformation space of hyperbolic structures.

For a directed polytope, we construct a colored operad whose Poincare-Hilbert series encodes certain operations on the cellular complex of the polytope. We conjecture that for a class of short polytopes the constructed operads are Koszul…

For the direct sum of several copies of sl_n, a family of Lie brackets compatible with the initial one is constructed. The structure constants of these brackets are expressed in terms of theta-functions associated with an elliptic curve.…

We show, among other things, that in most cases the gonality of a subcanonical curve in projective-three space is computable by multisecants.

For infinitely many $d$, Hassett showed that special cubic fourfolds of discriminant $d$ are related to polarized K3 surfaces of degree $d$ via their Hodge structures. For half of the $d$, each associated K3 surface $(S,L)$ canonically…

Within the framework of Berwald-Moor Geometry in H_3, the paper studies the construction of additive poly-angles (bingles and tringles). It is shown that, considering additiveness in the large, there exist an infinity of such poly-angles.

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly…

We describe a correspondence between Turaev surfaces of link diagrams on $S^2\subset S^3$ and special Heegaard diagrams for $S^3$ adapted to links.

Any planar shape $P\subset \mathbb{C}$ can be embedded isometrically as part of the boundary surface $S$ of a convex subset of $\mathbb{R}^3$ such that $\partial P$ supports the positive curvature of $S$. The complement $Q = S \setminus P$…

We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, together with a sequence of commuting…

Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an…

We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(\omega) with the Cantor set topology.

Using alternating Heegaard diagrams, we construct some 3-manifolds which admit diffeomorphisms such that the non-wandering sets of the diffeomorphisms are composed of Smale-Williams solenoid attractors and repellers, an interesting example…

We discuss the multiple summability of a multilinear map $T:X_1\times\cdots\times X_m\to Y$ when we have informations on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for…

In this Note, we will characterize the Poisson structures compatible with the canonical metric of $\reel^3$. We will also give some relvant examples of such structures. The notion of compatibility used in this Note was introduced and…

Given a sequence of oriented links L^1,L^2,L^3,... each of which has a distinguished, unknotted component, there is a decomposition of the 3-sphere naturally associated to it, which is constructed as the components of the intersection of an…

A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…