Fibrations of highly singular map germs

Abstract

We define local fibration structures for real map germs with strictly positive dimensional discriminant: a local fibration structure over the complement of the discriminant, and a complete local fibration structure which includes the stratified discriminant into the picture. We provide new classes of map germs endowed with such local fibration structures.

arXiv comment17 pages. Small changes: last part of the proof or Theorem 2.7 and the preliminary part of the proof of Theorem 4.3; updated references

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• On singular maps with local fibration
• Fibrations of tamely composable maps
• Polar degree and vanishing cycles
• Deformations with fibre constancy
• Milnor Fiber Consistency via Flatness
• On the Milnor fibration for $f(z)\bar{g}(z)$ II
• On the Milnor fibration for $f(\mathbf{z})\bar{g}(\mathbf{z})$
• Tame deformations of highly singular function germs
• Lipschitz Geometry of Mixed Pham-Brieskorn Singularities
• Results on Milnor Fibrations for mixed polynomials with non-isolated singularities
• Some remarks about $\rho$-regularity for real analytic maps