A compactification for the spaces of convex projective structures on manifolds

Details A compactification for the spaces of convex projective structures on manifolds A compactification for the spaces of convex projective structures on manifolds

2007-12-30

arxiv.org/abs/0801.0165v1

Mathematics

Geometric Topology

35 pages, 1 figure

Scientific paper

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 Teichm\"uller spaces.

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