Generalised Thurston-Bennequin invariants for real algebraic surface singularities

Details Generalised Thurston-Bennequin invariants for real algebraic surface singularities Generalised Thurston-Bennequin invariants for real algebraic surface singularities

2002-01-08

arxiv.org/abs/math/0201057v2

Mathematics

Geometric Topology

22 pages, TeX, 12 figures

Scientific paper

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch surface singularity. For such singularities, the value of the linking form is the Thurston-Bennequin number of the real link of the singularity. As a special case of unibranch surface singularities, the behaviour of the linking form is investigated on the Brieskorn double points x^m+y^n\pm z^2=0.

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