Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedron-like polyhedra

Details Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedron-like polyhedra Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedron-like polyhedra

2003-03-21

arxiv.org/abs/math/0303274v1

Mathematics

Differential Geometry

33 pages, 8 figures

Scientific paper

There are several ways of a construction of a boundary of a symmetric space using pencils of geodesics: the Karpelevich boundary, the visibility boundary, the associahedral boundary, and the sea urchin. We give explicit descriptions of these boundaries. We obtain some moduli space like polyhedra as sections of these compactifications by Cartan subspaces. For simplicity, we consider only the space $GL_n/O_n$ of ellipsoids in $R^n$.

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