arXiv · 1605.04590
We show the non-triviality of the mod 3 Chern class of degree 324 of the adjoint representation of the exceptional Lie group E_8.
Masaki Kameko. 2016-05-15. Mod 3 Chern classes and generators. https://doi.org/10.3792/pjaa.93.55
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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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