Strip maps of small surfaces are convex
classification
🧮 math.GT
keywords
stripconvexpuncturedsmallsurfaceborderedcomplexcomplexity
read the original abstract
The strip map is a natural map from the arc complex of a bordered hyperbolic surface $S$ to the vector space of infinitesimal deformations of $S$. We prove that the image of the strip map is a convex hypersurface when $S$ is a surface of small complexity: the punctured torus or thrice punctured sphere.
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