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math.GT2011★ 3 cited
Integrating curvature: from Umlaufsatz to J^+ invariant
Sergei Lanzat, Michael Polyak
Hopf's Umlaufsatz relates the total curvature of a closed immersed plane curve to its rotation number. While the curvature of a curve changes under local deformations, its integral…
math.GT2010★ 1 cited
Counting real curves with passage/tangency conditions
Sergei Lanzat, Michael Polyak
We study the following question: given a set P of 3d-2 points and an immersed curve G in the real plane R^2, all in general position, how many real rational plane curves of degree…