Patricia Cahn

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We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping " volcano unfolding. " These un-foldings keep the base intact, unfold the sides outward, splayed around the base, and attach the top to the tip of some side rib. Our result(More)
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on a surface. Turaev conjectured that his cobracket ∆(α) is zero if and only if α is a power of a simple class. Chas constructed examples that show Turaev's conjecture is, unfortunately, false. We define an operation µ in the spirit of(More)
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