Related papers: Restricted configuration spaces
We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}^{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic…
One of the primary methods of studying the topology of configurations of points in a graph and configurations of disks in a planar region has been to examine discrete combinatorial models arising from the underlying spaces. Despite the…
The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres. As a consequence, complex structures on $S^1\times S^7\times S^6$, and on $S^1\times S^3\times S^2$…
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
We present a systematic approach for constructing bar frameworks that are rigid but not first-order rigid, using constrained optimization. We show that prestress stable (but not first-order rigid) frameworks arise as the solution to a…
The method of constrained Hamiltonian systems can be used to reduce Fock modules. It is applied to the Virasoro algebra, where a possibly new realization is found.
We consider the problem of realizing a group as the fundamental group of a graph of groups where the vertex groups are restricted to certain classes (for example, coming from a certain finite list of groups, or having bounded geometric…
The rational homology of unordered configuration spaces of points on any surface was studied by Drummond-Cole and Knudsen. We compute the rational cohomology of configuration spaces on a closed orientable surface, keeping track of the mixed…
We use function field analytic number theory to establish the irreducibility and dimension of the moduli space that parameterises morphisms of fixed degree from $\mathbb{P}^2$ to an arbitrary smooth hypersurface of sufficiently small…
Tree-graded spaces are a generalization of $\mathbb{R}$-trees and play an important role in describing the large-scale geometry of relatively hyperbolic groups. We consider a subclass of tree-graded spaces that we call "disjointly…
We explore the topology of configuration spaces of hard disks experimentally, and show that several changes in the topology can already be observed with a small number of particles. The results illustrate a theorem of Baryshnikov, Bubenik,…
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…
In this paper we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made…
One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of $\mathbb{F}_q^n$,…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not…
We construct manifold structures on various sets of solutions of the general relativistic initial data sets.
It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…