Smooth Knot Limit Sets of the Complex Hyperbolic Plane

TL;DR

This paper proves that regular knots embedded as limit sets of discrete groups in the boundary of the complex hyperbolic plane are either chains or R-circles, revealing a geometric classification of such knots.

Contribution

It establishes a classification theorem for regular knots as limit sets in the complex hyperbolic plane boundary, identifying them as either chains or R-circles.

Findings

Limit sets of discrete subgroups are either chains or R-circles.

Regular C2 knots in the boundary are constrained to these two types.

Provides a geometric characterization of knot limit sets in complex hyperbolic geometry.

Abstract

It is shown that if a regular knot of class C2 is embedded in the boundary of the complex hyperbolic plane as the limit set of a discrete subgroup of PU(2, 1) then it is either a chain or an R-circle.