The configuration-spaces tag has no wiki summary.
41
votes
2answers
947 views
How many unit cylinders can touch a unit ball?
What is the maximum number $k$ of unit-radius cylinders with mutually disjoint interiors that can touch a unit ball?
By a cylinder I mean a set congruent to the Cartesian product of a line and a ...
1
vote
0answers
80 views
On 'Very Movable' Geometric Configurations (Configurations with a large degree of freedom)
Let $C$ be an $(n_r, b_k)$ combinatorial configuration that admits a geometric realization in the plane. I'm interested in the maximum number of points/lines $M$ of $C$ we can place in general ...
4
votes
2answers
365 views
The example of mechanical system that has a Mobius strip as their configuration space
Can you give examples for mechanical system that has a Mobius strip as their configuration space?
15
votes
2answers
438 views
Distinct manifolds with the same configuration spaces?
For a space $X$, let $C_k X$ denote the space of configurations of $k$ distinct unordered points in $X$.
What is an example of a pair of smooth manifolds $M$ and $N$ that are not homeomorphic but ...
5
votes
4answers
423 views
Configuration topos?
Let ${\bf Fin}$ denote the category of finite sets. If $X$ is a topological space, then for any natural number $k\in{\mathbb N}$, the slice category ${\bf Fin}/X$ contains the configuration space ...
8
votes
3answers
342 views
Configuration spaces of the torus
I would like a reference that calculates the rational homology of the unordered configuration spaces of the torus.
2
votes
1answer
152 views
holomorphic automorphisms of universal cover of configuration spaces
Hello everyone,
I have been trying (without success) to determine the following. Let $P$ denote the space of monic polynomials of degree $n$ with complex coefficients, which have distinct roots. It ...
5
votes
1answer
242 views
Spaces parametrizing ramified covers of surfaces
Let $\Sigma$ be a surface (let's say oriented and of finite type). We can consider the configuration space $F(\Sigma,n)$ of $n$ ordered distinct points on $\Sigma$, i.e. $\Sigma^n\setminus \Delta$ ...
10
votes
4answers
597 views
Beginning reference for configuration spaces
In my mathematical reading and thoughts, I keep running across the notion of configuration spaces, and while I essentially understand the idea behind them, I don't have much intuition for them (not ...
9
votes
2answers
525 views
Configuration spaces and non homeomorphic vector bundles
Given two complex line bundles over the complex projective line ${\mathbb CP}^1$, prove or disprove that their total spaces are homeomorphic if and only if their Chern numbers are equal up to sign.
...
8
votes
1answer
533 views
Orbifold fundamental group and configuration space
Hi,
I'm not very familiar with (even simple examples of) orbifolds, so my first question is:
Let $C_2$ be $\mathbb{C}$ with one cone singularity at 0 of index 2. What is the fundamental group of ...
3
votes
1answer
505 views
Almost-direct product and 1-formality
Hi everyone,
Let $G$ be a finitely presented group. To $G$ is associated in a functorial way a Malcev Lie algebra which can be constructed in several equivalent ways. Roughly speaking, it is the ...
6
votes
3answers
493 views
Relation between cohomology of ordered and unordered configuration spaces?
For any manifold $M$, the unordered configuration space of $k$ points is obtained as a quotient of ordered configuration space of $k$ points by the group action of symmetric group on $k$ letters. Does ...
20
votes
3answers
881 views
Configuration space of little disks inside a big disk
The space of configurations of $k$ distinct points in the plane
$$F(\mathbb{R}^2,k)=\lbrace(z_1,\ldots , z_k)\mid z_i\in \mathbb{R}^2, i\neq j\implies z_i\neq z_j\rbrace$$
is a well-studied object ...
7
votes
1answer
298 views
Aspherical homotopy orbit space of configurations on the 2-sphere
The group SO(3) acts naturally on $S^2$ and thus on $Conf(S^2, q)$, the configuration space of $q$ distinct points on the 2-sphere, via the diagonal action on $S^2 \times...\times S^2$. This is a ...
10
votes
2answers
940 views
The fibers of M_{g,n} \to M_g and the Fulton-MacPherson compactification
Let $g \geq 2$, and consider the moduli space $\bar M_{g,n}$ of stable n-pointed curves of genus g. There is a natural forgetful map to $\bar M_g$, which forgets the markings and contracts any ...
16
votes
1answer
767 views
Fundamental groups of the spaces of rational functions
Here is a question which I asked myself (and couldn't answer) while reading "The topology of spaces of rational functions" by G. Segal.
Let $X$ be a smooth complete complex curve (=a compact Riemann ...
3
votes
1answer
189 views
A k-component link defines a map T^k --> Conf_k S^3. Does the homotopy type capture Milnor's invariants?
A k-component link defines a map T^k --> Conf_k S^3. Does the homotopy type of this map capture the Milnor invariants?
Some ...
