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Left-invariant Riemannian distances on higher-rank Sol-type groups.

Daniel Levitin ⟨dlevitin@wisc.edu⟩

Abstract:

Describing the coarse geometry of solvable groups is one of the major projects of geometric group theory. One solvable group whose geometry is well-understood is Sol, a rank-1 group foliated by two families of hyperbolic planes. More generally, Le Donne, Pallier, and Xie recently described the geodesics in Sol-type groups, which are the rank-1 solvable groups foliated by a pair of negatively-curved spaces. Leveraging this description, they show that all left-invariant Riemannian distances on a Sol-type group are roughly similar. In this talk, I will describe the coarse geometry of the broader class of higher-rank Sol-type groups, and discuss my generalization of Le Donne-Pallier-Xie’s result to certain distances on these groups.

Scheduled for: 2025-03-07 03:55 PM: Daniel Levitin in Forbes 2070E

Status: Accepted

Collection: Geometric Group Theory

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