Geodesics and Visual boundary of Horospherical Products
Tom Ferragut
TL;DR
This paper explores the geometric structure of horospherical products, detailing their distances, geodesics, and visual boundaries, with applications to various discrete and continuous groups.
Contribution
It provides a comprehensive description of the geometry of horospherical products, including their geodesics and boundaries, unifying discrete and continuous examples.
Findings
Characterization of distances and geodesics in horospherical products
Description of the visual boundary for these geometric spaces
Application to Cayley graphs of lamplighter groups and solvable Lie groups
Abstract
We study the geometry of horospherical products by providing a description of their distances, geodesics and visual boundary. These products contains both discrete and continuous examples, including Cayley graphs of lamplighter groups and solvable Lie groups of the form IR semi-direct product with (N1 xN2), where N1 and N2 are two simply connected, nilpotent Lie groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Algebra and Geometry