A compactification for the spaces of convex projective structures on manifolds

2007/12/30 by Daniele Alessandrini, Alessandrini, Daniele
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT

paper · pdf · doi:10.48550/arxiv.0801.0165

35 pages, 1 figure

arxiv created 2007/12/30 · arxiv updated 2009/12/01

Abstract

In this paper we construct a compactification for the parameter space of convex projective structures on a fixed n-manifold M. This parameter space is a closed semi-algebraic subset of the variety of characters of representations of the fundamental group of M in SL_n+1(R). The boundary is the inverse limit of an inverse system of logarithmic limit sets of this semi-algebraic set, in a sense it is the tropicalization of the parameter space. The interpretation of the boundary points can also be given using tropical geometry. This construction is a generalization of the construction of compactification of the Teichmüller spaces.

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• Tropicalization of group representations

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