Relative (non-)formality of the little cubes operads and the algebraic\n Cerf Lemma

2014/08/30 by Victor Tourtchine, Thomas Willwacher, Tourtchine, Victor +1 · 4 citations
Mathematics · Medicine · #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1409.0163

openalex publication_date 2014/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the operad maps E_n\→ E_n+k are formal over the reals\nfor k\≥ 2 and non-formal for k=1. Furthermore we compute the cohomology\nof the deformation complex of the operad maps E_n\→ E_n+1, proving an\nalgebraic version of the Cerf Lemma.\n

Cited by

• Graphical configuration spaces, Contractads and Formality
• The rational homotopy of mapping spaces of E_n operads
• Oriented hairy graphs and moduli spaces of curves
• Hochschild-Pirashvili homology on suspensions and representations of Out(F_n)

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• Formality of the little N-disks operad
• Equivariant formality of the little disks operad
• Universal Properties of Variations of the Little Cubes Operads
• The intrinsic formality of E_n-operads
• Formality of little disks and algebraic geometry