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Abstract |
If $M$ is a manifold (or even a topological space), the configuration space
$F(M,k)$ is the space of $k$ distinct ordered points in $M$. For example, the space $F(\mathbb R^3,k)$ represents the space of possible configurations of $k$ objects in space. First we consider the special case of $F(\mathbb R^2, k)$ and describe its cohomology and homotopy groups, and its connection with the braid group $P_k$. We then move on to discuss the following two actively researched problems:
1) When is $F(M,k)$ invariant under homotopy?
2) Find an algebraic model for $F(M,k)$.
The present research is joint work with Pascal Lambrechts. |
