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arXiv · 1410.3316

A New Conjecture, a New Invariant, and a New Non-splitting Result

David B. Massey
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Abstract

We prove a new non-splitting result for the cohomology of the Milnor fiber, reminiscent of the classical result proved independently by Lazzeri, Gabrielov, and Lê in 1973-74. We do this while exploring a conjecture of Bobadilla about a stronger version of our non-splitting result. To explore this conjecture, we define a new numerical invariant for hypersurfaces with $1$-dimensional critical loci: the beta invariant. The beta invariant is an invariant of the ambient topological-type of the hypersurface, is non-negative, and is algebraically calculable. Results about the beta invariant remove the topology from Bobadilla's conjecture and turn it into a purely algebraic question.

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David B. Massey. 2015-04-27. A New Conjecture, a New Invariant, and a New Non-splitting Result. https://arxiv.org/abs/1410.3316

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