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Published in:
2017 | OriginalPaper | Chapter
A New Conjecture, a New Invariant, and a New Non-splitting Result
Author : David B. Massey
Published in: Singularities in Geometry, Topology, Foliations and Dynamics
Publisher: Springer International Publishing
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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 Fernández de 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.