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Hodge theory and the art of paper folding. (English) Zbl 0961.32026

From the text: Using Hodge theory and \(L^2\)-cohomology we study the singularities and topology of configuration and moduli spaces of polygonal linkages in the 2-sphere. As a consequence we describe the local deformation space of a folded paper cone in \(\mathbb{R}^3\).
This is a part of a series of our papers [M. Kaperovich and J. J. Millson, J. Diff. Geom. 44, No. 3, 479-513 (1996; Zbl 0889.58017), Topology 35, No. 4, 1085-1106 (1996; Zbl 0855.32013), Compos. Math. 103, No. 3, 287-317 (1996; Zbl 0872.53035) and C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 8, 871-876 (1997; Zbl 0948.20023)] where we study interrelations between members of
– configuration spaces of geometric objects
– algebraic varieties
– representation varieties of groups.

MSC:

32S30 Deformations of complex singularities; vanishing cycles
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