The cat-bat map, the figure-eight knot, and the five orbifolds

TL;DR

This paper explains how certain exceptional surgeries relate the suspension of the cat-bat map to unit tangent bundles of hyperbolic orbispheres, illustrating connections between dynamical systems and 3-dimensional topology.

Contribution

It provides an exposition on how exceptional surgeries link specific dynamical maps to hyperbolic orbifolds, enriching understanding of 3-manifold topology.

Findings

Identification of surgeries connecting the cat-bat map suspension to hyperbolic orbispheres

Explanation of the relationship between the figure-eight knot and orbifold structures

Insights into the topology of five orbifolds related to these surgeries

Abstract

These are expository notes in which we explain how one can see some exceptional surgeries connecting the suspension of the cat-bat map and the unit tangent bundles to some hyperbolic orbispheres.