RELATIVE (NON-)FORMALITY OF THE LITTLE CUBES OPERADS AND THE ALGEBRAIC CERF LEMMA.

It is shown that the operad maps En → En+k are formal over the reals for k ≥ 2 and nonformal for k = 1. Furthermore we compute the homology of the deformation complex of the operad maps En → En+1, proving an algebraic version of the Cerf lemma. [ABSTRACT FROM AUTHOR]