Real Algebraic and Analytic Geometry |

Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem.

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Submission: 2007, October 1.

*Abstract:
Let f be a definable function, enough differentiable. Under the
condition of having strongly isolated singularities at infinity at a
regular value c we give a sufficient condition expressed in terms of
the total absolute curvature function to ensure the local triviality of
the function f over a neighbourhood of c and doing so providing the
tame version of Parusinski's Theorem on complex polynomials with
isolated singularities at infinity.*

Mathematics Subject Classification (2000): 58K05, 03C64, 14B05.

Keywords and Phrases: generalised critical values, bifurcation values, o-minimal structure, relative conormal space, total absolute curvature, polar curves.

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