Related papers: Topological spherical space forms
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
We classify orthogonal actions of finite groups on Euclidean vector spaces for which the corresponding quotient space is a topological, homological or Lipschitz manifold, possibly with boundary. In particular, our results answer the…
In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…
We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for compact effective group actions on spheres and provide…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…
We classify all spherical 2-designs that arise as orbits of finite group actions on real inner product spaces. Although it is well known that such designs can occur in representations without trivial components, we give a complete…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
This is a review paper about symmetric products of spaces $SP^n(X):= X^n/S_n$. We focus our attention on the symmetric products of 2-manifolds and make a journey through selected topics of algebraic topology, algebraic geometry,…
\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…
The notion of G-structure is defined and various geometrical and topological aspects of such structures are discussed. A particular chain of subgroups in the affine group for Minkowski space is chosen and the canonical geometrical and…
We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…
Magnetic vortices and skyrmions are typically characterized by distinct topological invariants. This work presents a unified approach for the topological classification of these textures, encompassing isolated objects and configurations…