Pants immersed in hyperbolic 3-manifolds

TL;DR

This paper classifies immersed thrice-punctured spheres in cusped hyperbolic 3-manifolds, showing they are either embedded or have a single clasp after specific Dehn fillings, advancing understanding of 3-manifold topology.

Contribution

It provides a classification of immersed thrice-punctured spheres in cusped hyperbolic 3-manifolds, identifying conditions under which they are embedded or clasped.

Findings

Immersed thrice-punctured spheres are either embedded or clasped.

Clasped spheres occur after Dehn filling on Whitehead link complement.

Classification aids in understanding 3-manifold topology.

Abstract

We show that an immersed thrice-punctured sphere in a cusped orientable hyperbolic 3-manifold is either embedded or has a single clasp in a manifold obtained by hyperbolic Dehn filling on a cusp of the Whitehead link complement.