Singular open book structures from real mappings
Mihai Tibar, Ying Chen, Raimundo N. Ara\'ujo dos Santos

TL;DR
This paper extends Milnor's theorem to nonisolated singularities in real mappings, identifying new classes of real analytic mappings with singularities that still admit Milnor fibrations and open book structures.
Contribution
It introduces generalized Milnor fibrations for germs with nonisolated singularities, expanding the understanding of open book structures in real analytic mappings.
Findings
Established Milnor fibrations for new classes of real mappings with nonisolated singularities.
Proved extensions of Milnor's theorem applicable to germs with positive dimensional singular loci.
Identified conditions under which real analytic mappings admit open book structures with singular binding.
Abstract
We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings with positive dimensional singular locus , for which the Milnor fibration exists and yields an open book structure with singular binding.
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