Related papers: Maps to spaces in the genus of infinite quaternion…

It is shown that only countably many spaces in the genus of $\hpinfty$, the infinite quaternionic projective space, can admit essential maps from $\cpinfty$, the infinite complex projective space. Examples of countably many homotopically…

Using quaternions and octonions, we construct some maps from the Grassmannian of 2-dimensional planes of $\mathbb{R}^n$, $\mathrm{Gr}_2(\mathbb{R}^n)$, to the projective space $\mathbb{R}\mathrm{P}^k$, for certain values of $n$ and $k$. All…

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…

We study the homotopy types of certain spaces closely related to the spaces of algebraic (rational) maps from the $m$ dimensional real projective space into the $n$ dimensional complex projective space for $2\leq m\leq 2n$ (we conjecture…

We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial…

We show that closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy…

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence…

We find large classes of injective and projective $p$-multinormed spaces. In fact, these classes are universal, in the sense that every $p$-multinormed space embeds into (is a quotient of) an injective (resp. projective) $p$-multinormed…

We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.

We use obstruction theory based on the unstable Adams spectral sequence to construct self maps of finite quaternionic projective spaces. As a result, a conjecture of Feder and Gitler regarding the classification of self maps up to homology…

Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.

The authors establish a relation of the theory of varieties with degenerate Gauss maps in projective spaces with the theory of congruences and pseudocongruences of subspaces and show how these two theories can be applied to the construction…

We consider the inclusion of the space of algebraic (regular) maps between real algebraic varieties in the space of all continuous maps. For a certain class of real algebraic varieties, which include real projective spaces, it is well known…

We extend T. Y. Thomas's approach to the projective structures, over the complex analytic category, by involving the $\rho$-connections. This way, a better control of the projective flatness is obtained and, consequently, we have, for…

In this paper, all finite groups whose commuting (non-commuting) graphs can be embed on the plane, torus or projective plane are classified.

This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

The problem of approximating the infinite dimensional space of all continuous maps from an algebraic variety $X$ to an algebraic variety $Y$ by finite dimensional spaces of algebraic maps arises in several areas of geometry and mathematical…

Let $[\rho_{i_k},[\rho_{i_{k-1}},...,[\rho_{i_{1}}, \rho_{i_2}] ...]]$ be an iterated commutator of self-maps $\rho_{i_j} : \Sigma {\Bbb H}P^\infty \to \Sigma {\Bbb H}P^\infty, j = 1,2, ..., k$ on the suspension of the infinite quaternionic…

Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the `quaternionic-like manifolds'. These contain, as…