Configuration spaces of manifolds with boundary/ Ricardo Campos et. al.

Includes index and bibliography

Background and recollection -- Poincare- Lefschetz duality models -- Configuration spaces, their compactifications, and algebraic structures -- Construction of propagators -- Graphical models- recollections -- A model or SFMM -- A model for mFM and aFMaM -- Relation and small models for "good" spaces -- Chomology of some graph complexes

We study ordered configuration spaces of compact manifolds with boundary. We show that for a large class of such manifolds, the real homotopy type of the configuration spaces only depends on the real homotopy type of the pair consisting of the manifold and its boundary. We moreover describe explicit real models of these configuration spaces using three different approaches. We do this by adapting previous construction for configuration spaces of closed manifolds which relied on Kontsevich's proof of the formality of the little disks operads. We also prove that our models are compatible with the richer structure of configuration spaces respectively a module over the swiss- Cheese operad, a module over the associative algebra of configurations in a collar around the boundary of the manifold, and a module over the little diks operad.