Title

On Primeness of Labeled Oriented Trees

Document Type

Article

Publication Date

3-21-2012

Abstract

Knot complements are aspherical. Whether this extends to ribbon disc complements, or, equivalently, to standard 2-complexes of labeled oriented trees, remains unresolved. It is known that prime injective labeled oriented trees are diagrammatically reducible, that is, aspherical in a strong combinatorial sense. We show that arbitrary prime labeled oriented trees need not be DR. We conjecture that all injective labeled oriented trees are aspherical and prove the conjecture under natural conditions.