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 $H^*(\mathcal{Z}_K;\mathbb{Q})$ for arbitrary $n$ and in arbitrary cohomological degrees, removes this connectivity restriction entirely.
From: Alexander I. Suciu [view email]
[v1]
Sun, 10 May 2026 01:48:37 UTC (25 KB)
[v2]
Wed, 17 Jun 2026 22:57:50 UTC (32 KB)
[v3]
Mon, 20 Jul 2026 04:45:31 UTC (32 KB)
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