The degeneration of the boundary of the Milnor fibre to the link of\n complex and real non-isolated singularities

2012/09/05 by Neto, Aurélio Menegon, José Seade, Seade, José
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1209.1066

Abstract

We study the boundary of the Milnor fibre of real analytic singularities f:\n( bR^m,0) \→ ( bR^k,0), m\≥ k, with an isolated critical value and the\nThom a_f-property. We define the vanishing zone for f and we give necessary\nand sufficient conditions for it to be a fibre bundle over the link of the\nsingular set of f^-1(0). In the case of singularities of the type fgbar:\n( bCⁿ,0) \→ ( bC,0) with an isoalted critical value, f, g holomorphic, we\nfurther describe the degeneration of the boundary of the Milnor fibre to the\nlink of fgbar. As a milestone, we also construct a L ^e's polyhedron for\nreal analytic singularities of the type fgbar: ( bC²,0) \→ ( bC,0) such\nthat either f or g depends only on one variable.\n

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