EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

Author(s)

Araujo dos Santos, R. N. ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Rocky Mountain Journal of Mathematics; v. 42, n. 2, p. 439-449, 2012.
• Web of Science Citations: 2

Abstract

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \textbackslash{} K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \textbackslash{} K-epsilon -> S-1. (AU)

• FAPESP's process: 09/14383-3 - Topology of real and complex singularities
• Grantee: Raimundo Nonato Araújo dos Santos
• Support Opportunities: Regular Research Grants