Related papers: Semiconfiguration Spaces of Planar Linkages
This paper studies the configuration space of all possible positions of a linkage in R^n. For example, it shows that for every compact algebraic set, there is a linkage whose configuration space is analytically isomorphic to a finite number…
We show that any compact connected semialgebraic set is the projection of a connected component of the configuration space of a linkage.
A $configuration$ of a linkage $\Gamma$ is a possible positioning of $\Gamma$ in $\mathbb{R}^d$ and the collection of all such forms the configuration space $\mathcal{C}(\Gamma)$ of $\Gamma$. We here introduce the notion of the $symmetric…
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case…
Configuration spaces form a rich class of topological objects which are not usually presented to an undergraduate audience. Our aim is to present configuration spaces in a manner accessible to the advanced undergraduate. We begin with a…
Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with…
We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…
We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the…
This paper studies the configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that,…
We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of the space of natural numbers.
A classification of semisimple algebras of vector fields on C^N that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local canonical form of semisimple Lie algebras of vector fields.
In this paper we study the spaces of $q$-tuples of points in a Euclidean space, without $k$-wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…
We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space $\mathbb{R}^d$, where points in each cluster satisfy a 'verticality' condition, depending on a decomposition $d=p+q$. We compute the…
The present work considers the properties of classes of generally convex sets in the plane known as $1$-semiconvex and weakly $1$-semiconvex. More specifically, the examples of open and closed weakly $1$-semiconvex but non $1$-semiconvex…
In this paper we put forward the definition of particular subsets on a unital C*-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order…
A point set $M$ in Euclidean plane is called an integral point set in semi-general position if all the distances between the elements of $M$ are integers, and $M$ does not contain collinear triples. We improve the lower bound for diameter…
A point set $M$ in the Euclidean plane is called a planar integral point set if all the distances between the elements of $M$ are integers, and $M$ is not situated on a straight line. A planar integral point set is called to be in…
In this paper we develop algorithms of finding homogeneous spaces of semisimple non-compact Lie groups which do not admit compact Clifford-Klein forms. We propose a computer program which checks if the given homogeneous space has a…
The main result in this paper is that the space of all smooth links in Euclidean 3-space isotopic to the trivial link of n components has the same homotopy type as its finite-dimensional subspace consisting of configurations of n unlinked…