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Singularity theory is concerned with the local and global structure of maps and spaces that occur in algebraic, analytic or differential geometric context. It uses methods from algebra, topology, algebraic geometry and complex analysis.
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András Némethi, Duco van Straten, Victor A. Vassiliev, Singularities. Oberwolfach Rep. 9 (2012), no. 3, pp. 2799–2866DOI 10.4171/OWR/2012/46