Pascal Lambrechts: Real homotopy type of configurations spaces in manifolds with boundary

ABSTRACT: For a manifold with boundary, M, the configuration space of k points in M is defined as

\(Conf(k,M) = \{ (x_1,...,x_k) \in M^k : x_i \not=x_j \textrm{ for } i\not=j \}.\)
We explain, for some class of manifolds with boundary, how one can obtain an algebraic model (in the sense of Sullivan) of the real homotopy type of Conf(k,M) out of a model of the pair \((M,\partial M)\). This extends recent results by Willwacher-Campo and Idrissi who have construct this model for compact manifolds without boundary.
Moreover, when the manifold is framed, we also obtain a model of the action of the Swiss-cheese operad on the spaces of configurations. The methods are based on the approach of Kontsevich to prove the formality of the little disk operad.
This is joint work with N. Idrissi.