Related papers: Some remarks about solenoids, 2
We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the…
Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential forms of n-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are…
We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and…
We examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…
This paper invents the notion of torified varieties: A torification of a scheme is a decomposition of the scheme into split tori. A torified variety is a reduced scheme of finite type over $\Z$ that admits a torification. Toric varieties,…
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…
We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
We report on the status of our search for quasi-topological solitons of various dimensions in realistic field theoretical models of condensed matter and of elementary particle physics.
We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…
Previous work of the author has developed coordinates on bundles over the classical Teichmueller spaces of punctured surfaces and on the space of cosets of the Moebius group in the group of orientation-preserving homeomorphisms of the…
When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse…
A 2-categorical generalisation of elementary topos is provided and some of the properties of the yoneda structure it generates are explored. Examples relevant to the globular approach to higher category theory are discussed. This paper also…
Under suitably nice conditions, given a coalgebra object in a tensor category we compute the layers of its coradical (socle) filtration.
All SL($n$) contravariant vector valuations on polytopes in $\mathbb R^n$ are completely classified without any additional assumptions. The facet vector is defined. It turns out to be the unique such valuation for $n\geq3$. In dimension…
We study some topological properties of attractors.
We introduce a particular family of two-dimensional surfaces in $\mathbb R^4$ which generalize the classical Dini surfaces in $\mathbb R^3$.
We construct complete, finite volume, 4-dimensional manifolds with sectional curvature $-1<K<0$ with cusp cross sections compact solvmanifolds.
Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling…
Here I present several theorems about trapezoids tilings. The first one is related to trapezoids with rational base relation, the other ones are related to those with base relation from quadratic number field.