arXiv · 0902.3576
We extend Tamarkin's formality of the little disk operad to the framed little disk operad.
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Pavol Severa. 2009-02-20. Formality of the chain operad of framed little disks. https://doi.org/10.1007/s11005-010-0399-z
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For every $n\geq 3$ and $s\geq 2$, we construct a homogeneous polynomial of degree $n(n+1)/2$ whose Milnor fiber is exactly $2s$-connected and whose rational cohomology contains a strictly defined nontrivial $n$-fold Massey product on classes of degree $2s+1$, implying that the Milnor fiber is non-formal, while attaining the Kato--Matsumoto connectivity bound. Our construction is based on the simplicial multiwedges of the nerve complexes of simple polytopes introduced by Limonchenko, combined with Suciu's realization of weighted homogeneous Milnor fibers. We thereby answer two problems posed by Suciu.
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