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 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.
Mathematics Subject Classification (2000). 32B15, 32C35, 32C18, 32B10.
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Massey, D.B. (2017). A New Conjecture, a New Invariant, and a New Non-splitting Result. In: Cisneros-Molina, J., Tráng Lê, D., Oka, M., Snoussi, J. (eds) Singularities in Geometry, Topology, Foliations and Dynamics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-39339-1_10
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DOI: https://doi.org/10.1007/978-3-319-39339-1_10
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-39338-4
Online ISBN: 978-3-319-39339-1
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