Complex singularities and contact topology

Popescu-Pampu, Patrick

Winter Braids VI (Lille, 2016), Winter Braids Lecture Notes (2016), Exposé no. 3, 74 p.

This text is a greatly expanded version of the mini-course I gave during the school Winter Braids VI organized in Lille between 22–25 February 2016. It is an introduction to the study of interactions between singularity theory of complex analytic varieties and contact topology. I concentrate on the relation between the smoothings of singularities and the Stein fillings of their contact boundaries. I tried to explain basic intuitions and facts in both fields, for the sake of the readers who are not accustomed with one of them.

Mots clés : Contact structure, complex singularity, cyclic quotient singularity, Gorenstein singularity, graph manifold, Hirzebruch-Jung singularity, Milnor fiber, minimally elliptic singularity, modification, normal singularity, plumbing, plurisubharmonic function, quotient singularity, Stein filling, rational surface singularity, resolution of singularities, smoothing, versal deformation.

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