# Questions tagged [configuration-space]

Configuration spaces refer to topological spaces that consist of ordered or unordered subsets of a topological space, of a given (finite) cardinality.

8 questions
Filter by
Sorted by
Tagged with
113 views

### Is the set of collections of directions satisfying the following convexity conditions “geometric”?

Let $X_n$ denote the set of all collections $(v_{ij})$ of points on the sphere $S^2$, for $1 \leq i,j \leq n$, $i \neq j$, such that: $v_{ji} = -v_{ij}$, the origin $O$ in $\mathbb{R}^3$ is in the ...
44 views

I am doing ex. 2.3(2) from Frankel's book "The geometry of Physics". He says to consider the tangent bundle to a manifold M and show: i) that under a change of coordinated in M, $\partial / \partial ... 1answer 53 views ### Fundamental groups of the configuration spaces of all triangles and right triangles This is a question from a past comprehensive exam: Consider triangles in the plane, with vertices given by non-colinear points as usual. The space$T$of all plane triangles can be given a natural ... 0answers 69 views ### Generalising dual triangulation of manifolds We know the following “geometric” version of Poincaré duality: Let$M$be a closed$m$-dimensional manifold and let$\mathfrak{X}_*$be a finite simplicial complex with$|\mathfrak{X}_*|=M$. We can ... 0answers 51 views ### Path-connected components of the configuration space$F_n(R^d)$[duplicate] Let$X$be a topological space, for$n \geq 1$we define$F_n(X) = \lbrace{ (x_1,...,x_n) \in X^n | x_i \neq x_j for i \neq j \rbrace} $the configuration space of n points of X. My question is ... 1answer 104 views ### Configurations whose convex hull contains the origin Let$x_1,\ldots,x_n$be$n$points in$\mathbb{R}^3$. Are there known necessary and sufficient conditions on the$x_i$'s so that the origin belongs to the convex hull of the$x_i\$'s? I did a (not so ...
Say you have three (distinct) points on the unit sphere in Euclidean space $$p_1, p_2, p_3 \in S^n = \{ x \in \mathbb R^{n+1} : |x| = 1 \}$$ I'd like to find, as efficiently and robustly as possible,...