Given Poincaré spaces and , we study the possibility of compressing embeddings of in down to embeddings of in . This results in a new approach to embedding in the metastable range both in the smooth and Poincaré duality categories.
"Embedding, compression and fiberwise homotopy theory." Algebr. Geom. Topol. 2 (1) 311 - 336, 2002. https://doi.org/10.2140/agt.2002.2.311