CV_{g,n}^* is the tropicalization of the complex manifold hT(V_{g,n}) of stable complex handlebodies, with a partial compactification that is a simply connected manifold with simple normal crossings boundary, generalizing Schottky and Outer space relationships to n punctures.
Introduction to Tropical Geometry (notes from the IMPA lectures in Summer 2007)
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abstract
These condensed notes treat some basic notions in Tropical Geometry (varieties, cycles, modifications, equivalence). These topics are to be extended, illustrated and included to the upcoming book project http://www.math.toronto.edu/mikha/book.pdf .
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Handlebodies, Outer space, and tropical geometry
CV_{g,n}^* is the tropicalization of the complex manifold hT(V_{g,n}) of stable complex handlebodies, with a partial compactification that is a simply connected manifold with simple normal crossings boundary, generalizing Schottky and Outer space relationships to n punctures.