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Topological problems in wave propagation theory and topological economy principle in algebraic geometry. (English) Zbl 0946.01011

Bierstone, Edward (ed.) et al., The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his 60th birthday, Toronto, Canada, June 15-21, 1997. Providence, RI: American Mathematical Society. Fields Inst. Commun. 24, 39-54 (1999).
Ockham’s razor, entia non sunt multiplicanda sine necessitate, is stood on its head: the simplest geometric construction always requires the full number of objects for topological reasons, and you can always have excess, but you may never have shortfall. The article is full of conjectures about the number of singular points (Cusps, criminal self-tangencies) required in geometric or wave constructions, and the topological reasons requiring at least the known minimum number of such objects. The article is deliberately informal.
For the entire collection see [Zbl 0929.00102].

MSC:

01A65 Development of contemporary mathematics
14-03 History of algebraic geometry
14H99 Curves in algebraic geometry
34B24 Sturm-Liouville theory
58C25 Differentiable maps on manifolds
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