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Relative (non-)formality of the little cubes operads and the algebraic Cerf lemma
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 140, Number 2, April 2018
- pp. 277-316
- 10.1353/ajm.2018.0006
- Article
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abstract:
It is shown that the operad maps $E_n\to E_{n+k}$ are formal over the reals for $k\geq 2$ and non-formal for $k=1$. Furthermore we compute the homology of the deformation complex of the operad maps $E_n\to E_{n+1}$, proving an algebraic version of the Cerf lemma.