Stretch laminations and hyperbolic Dehn surgery

TL;DR

This paper investigates the properties of maximal stretch laminations in hyperbolic 3-manifolds undergoing Dehn surgery, providing criteria for when these laminations consist solely of core curves and exploring their implications for fibrations.

Contribution

It introduces a criterion based on Thurston norm and slope length to identify when stretch laminations are unions of core curves, advancing understanding of hyperbolic Dehn surgery.

Findings

Existence of infinitely many fibrations with laminations having only closed leaves.

Criteria linking Thurston norm, Dehn filling slope length, and lamination structure.

Insights into non-maximal horospherical orbit closures in infinite cyclic covers.

Abstract

We study maximal stretch laminations associated to certain best Lipschitz circle valued maps in Dehn surgery families of hyperbolic 3-manifolds. For these maps, we give a criterion based on the Thurston norm and Dehn filling slope length to determine when such a stretch lamination is a union of Dehn filling core curves. We use this to show there exist infinitely many examples where the homotopy class of the circle valued map includes a fibration and where the laminations have only closed leaves. This gives information about non-maximal horospherical orbit closures in the infinite cyclic covers associated to these fibrations.