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- W1992329603 abstract "We study Milnor fibrations of real analytic maps [Formula: see text], n ≥ p, with an isolated critical value. We do so by looking at a pencil associated canonically to every such map, with axis V = f -1 (0). The elements of this pencil are all analytic varieties with singular set contained in V. We introduce the concept of d-regularity, which means that away from the axis each element of the pencil is transverse to all sufficiently small spheres. We show that if V has dimension 0, or if f has the Thom a f -property, then f is d-regular if and only if it has a Milnor fibration on every sufficiently small sphere, with projection map f/‖f‖. Our results include the case when f has an isolated critical point. Furthermore, we show that if f is d-regular, then its Milnor fibration on the sphere is equivalent to its fibration on a Milnor tube. To prove these fibration theorems we introduce the spherefication map, which is rather useful to study Milnor fibrations. It is defined away from V; one of its main properties is that it is a submersion if and only if f is d-regular. Here restricted to each sphere in ℝ n the spherefication gives a fiber bundle equivalent to the Milnor fibration." @default.
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- W1992329603 date "2010-04-01" @default.
- W1992329603 modified "2023-09-30" @default.
- W1992329603 title "MILNOR FIBRATIONS AND d-REGULARITY FOR REAL ANALYTIC SINGULARITIES" @default.
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- W1992329603 doi "https://doi.org/10.1142/s0129167x10006124" @default.
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