Work

Homogeneous Milnor fibers and Kato--Matsumoto bounds via simplicial multiwedges

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11396

Authors: Ishikawa, Masaharu, Nguyen, Tat-Thang

Institutions: Keio University, Institute of Mathematics, Vietnam Academy of Science and Technology

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212245986

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