Related papers: Cellular structures, quasisymmetric mappings, and …
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged…
The fibre bundles adjoint to generalized almost quaternionic structures are studied. The most important classes of generalized almost quaternionic manifolds are considered.
Whole-cell computational models aim to predict cellular phenotypes from genotype by representing the entire genome, the structure and concentration of each molecular species, each molecular interaction, and the extracellular environment.…
We find geometric conditions on a four-dimensional almost Hermitian manifold under which the almost complex structure is a harmonic map or a minimal isometric imbedding of the manifold into its twistor space.
The optimal use of resources has motivated the engineering community to employ controlled distribution of material within their structural designs, often relying on cellular and lattice porous structures. In this research work, a…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…
In this paper we give a summary of the comparisons between different definitions of so-called (\infty,1)-categories, which are considered to be models for \infty-categories whose n-morphisms are all invertible for n>1. They are also, from…
This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with…
In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in…
Often it is possible to equip the space of all cone geodesics of a strongly convex cone structure with the structure of a smooth contact manifold. This generalizes the analogous notions for the space of light rays of a Lorentzian spacetime.…
Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…
In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong…
We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion--free and some types of them have to be locally flat. We prove that each symmetry…
Following the analogy between algebras (monoids) and monoidal categories the construction of nucleus for non-associative algebras is simulated on the categorical level. Nuclei of categories of modules are considered as an example.