6
votes
1answer
108 views

An analogue of cabling for configuration spaces

There is a well-known operation known as cabling for knots, and also for braid groups, where it is a homomorphism $$\beta_k \times \beta_\ell \longrightarrow \beta_{k\ell}$$ given by thickening up the ...
8
votes
3answers
381 views

Configuration spaces of the torus

I would like a reference that calculates the rational homology of the unordered configuration spaces of the torus.
10
votes
4answers
658 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 ...
20
votes
3answers
919 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 ...