Generalized cusps in real projective manifolds: classification

We study a generalized cusp C that is diffeomorphic to [0,∞) times a closed Euclidean manifold. Geometrically, C is the quotient of a properly convex domain in RPn by a lattice, Γ , in one of a family of affine Lie groups G(ψ) , parameterized by a point ψ in the (dual closed) Weyl chamber for SL(n+1,R) , and Γ determines the cusp up to equivalence. These affine groups correspond to certain fibered geometries, each of which is a bundle over an open simplex with fiber a horoball in hyperbolic space, and the lattices are classified by certain Bieberbach groups plus some auxiliary data. The cusp has finite Busemann measure if and only if G(ψ) contains unipotent elements. There is a natural underlying Euclidean structure on C unrelated to the Hilbert metric.

• Publication year

  2017

• Venue

  Journal of Topology

• Publication date

  2017-10-09

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1112/topo.12161arXiv 1710.03132
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  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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