What is... hierarchical hyperbolicity?

Abstract

This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.

Figures (5)

• Figure 1: The definition of $\delta$-thin (left), and a triangle in a tree (right).
• Figure 2: Jacob Russell's schematic of a tree of flats, embedded non-isometrically into $\mathbb{R}^3$. The closest point projection of the green point to the centrally-drawn flat is the purple point.
• Figure 3: The second toy example (top) and the metric spaces for each domain (bottom), decorated with three arbitrary points and their coordinates.
• Figure 4: The $\rho$ points.
• Figure 5: If $U$ and $V$ are transverse, $(x_U, x_V)$ must be in the shaded region of $\mathcal{C} U \times \mathcal{C} V$.