The homotopy type of the complement of a subpolyhedron in a manifold
by
Pascal Lambrechts
Laboratoire de Mathématiques, Université d'Artois, Faculté Jean Perrin, rue Jean Souvraz SP18, F-62307 Lens cedex, France
Coauthors: Donald Stanley, Lucile Vandenbroucq

Let M be a closed manifold and let K be a subpolyhedron. We will show in this talk how it is possible to recover the rational homotopy type of the complement M\K from the homotopy class of the embedding K --> M, at least when the codimension of the embedding is large enough. We will also discuss different applications of this result: to symplectic topology, to configuration spaces and to embeddings up to homotopy type.

This work is in collaboration with Donald Stanley and Lucile Vandenbroucq.

Date received: May 7, 2001