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Generalised Thurston-Bennequin invariants for real algebraic surface singularities

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Abstract

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 singularity of a real algebraic surface. 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 xm+yn±z2=0.

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  1. Mathematics Department, Boğaziçi University, 34342, Bebek, İstanbul, Turkey

    Ferit Öztürk

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  1. Ferit Öztürk
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Öztürk, F. Generalised Thurston-Bennequin invariants for real algebraic surface singularities. manuscripta math. 117, 273–298 (2005). https://doi.org/10.1007/s00229-005-0549-2

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  • DOI: https://doi.org/10.1007/s00229-005-0549-2

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