Related papers: Cellular structures, quasisymmetric mappings, and …
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
Let $M$ denote a two-dimensional Moore space (so $H_2(M; \Z) = 0$), with fundamental group $G$. The $M$-cellular spaces are those one can build from $M$ by using wedges, push-outs, and telescopes (and hence all pointed homotopy colimits).…
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Topologically stable cellular partitions of D dimensional spaces are studied. A complete statistical description of the average structural properties of such partition is given in term of a sequence of D/2-1 (or (D-1)/2) variables for D…
We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.
An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is…
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
A simplified view of the space of optimised stellarators has the potential to guide and aid the design efforts of magnetic confinement configurations suitable for future fusion reactors. We present one such view for the class of…
The two pillars of Algebraic topology - Homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study…
We study fibred spaces with fibres in a structure category $\V$ and we show that cellular approximation, Blakers--Massey theorem, Whitehead theorems, obstruction theory, Hurewicz homomorphism, Wall finiteness obstruction, and Whitehead…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
In this survey article we discuss certain homotopy coherent enhancements of the coalgebra structure on cellular chains defined by an approximation to the diagonal. Over the rational numbers, $C_\infty$-coalgebra structures control the…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.