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Local/global Singularity Theory is concerned with the local/global structure of maps and spaces that occur in diﬀerential topology or theory of algebraic or analytic varieties. It uses methods from algebra, topology, algebraic geometry and multi-variable complex analysis.
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Duco van Straten, Victor A. Vassiliev, András Némethi, Singularities. Oberwolfach Rep. 6 (2009), no. 3, pp. 2405–2470