Related papers: Invariant Generalized Complex Structures on Partia…

A $G$-invariant version of definable Tietze extension theorem for definably complete structures is proved when a definably compact definable topological group $G$ acts definably and continuously on the definable set.

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

We introduce a class of perverse sheaves on a partial flag manifold of a connected reductive group G defined over a finite field which are equivariant under the action of the group of rational points of G. The definition of this class is…

We show that extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure. This result stems from a new proof of the fact that a closed real-hyperbolic 4-manifold cannot support a complex structure.…

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…

The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…

Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance…

The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a…

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…

It is a well known fact that every embedded symplectic surface $\Sigma$ in a symplectic 4-manifold $(X^4,\omega)$ can be made $J$-holomorphic for some almost-complex structure $J$ compatible with $\omega$. In this paper we investigate when…

A generalized complex structure is called stable if its defining anticanonical section vanishes transversally, on a codimension-two submanifold. Alternatively, it is a zero elliptic residue symplectic structure in the elliptic tangent…

We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold $M$ the open manifold $M\times\r$ has infinitely many different smooth structures. Another consequence of Furuta's result is…

We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives. This generalizes the classical…

We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized K\"ahler structures. By considering the commutator $Q$ of the two associated almost complex structures…

We explore the class of triples (M, nabla, P) where M is a manifold, nabla is an affine connection in M and P is a G-structure in M. Inside this class there are infinitesimally homogeneous manifolds, characterized by having G-constant…

In this letter we proved this theorem: \emph{if $F$ be a holomorphic mapping of $T_{\Omega}$ to a mapping manifold $X$ such that for every compact subset $K\subset \Omega$ the mapping $F$ is uniformly continues on $T_{K}$ and $F(T_{K})$ is…

We introduce the concept of generalized almost plastic structure, and, on a pseudo-Riemannian manifold endowed with two $(1,1)$-tensor fields satisfying some compatibility conditions, we construct a family of generalized almost plastic…

A colored complex of type $\mathbf{a} = (a_1, \dots, a_n)$ is a simplicial complex ${\Delta}$ on a vertex set $V$, together with an ordered partition $(V_1, \dots, V_n)$ of $V$, such that every face $F$ of ${\Delta}$ satisfies $|F \cap V_i|…