Highly connected non-formal Milnor fibers via polyhedral products

Abstract

We show that the realization theorem of Fernández de Bobadilla, which identifies the Milnor fiber of a weighted-homogeneous polynomial with the complement of a germ of analytic set, can be combined with the systematic Massey product constructions of Grbić-Linton for moment-angle complexes ${\mathcal{Z}}_K={\mathcal{Z}}_K(D^2,S^1)$ to produce weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal. The original application of this strategy, due to Fernández de Bobadilla, used the Denham-Suciu classification of lowest-degree triple Massey products and yielded only 2-connected non-formal Milnor fibers. The Grbić-Linton framework, which constructs non-trivial $n$-fold Massey products in $H^{\ast }({\mathcal{Z}}_K;\mathbb{Q})$ for arbitrary $n$ and in arbitrary cohomological degrees, removes this connectivity restriction entirely.

arXiv comment23 pages, accepted for publication in the European Journal of Mathematics, Mihai Tibăr Memorial Collection

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