TY - JOUR
T1 - On primeness of labeled oriented trees
AU - Harlander, Jens
AU - Rosebrock, Stephan
PY - 2012/7
Y1 - 2012/7
N2 - 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.
AB - 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.
KW - 2-complex
KW - asphericity
KW - diagrammatic reducibility
KW - labeled oriented tree
KW - Wirtinger presentation
UR - http://www.scopus.com/inward/record.url?scp=84860535475&partnerID=8YFLogxK
U2 - 10.1142/S0218216512500770
DO - 10.1142/S0218216512500770
M3 - Article
AN - SCOPUS:84860535475
SN - 0218-2165
VL - 21
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 8
M1 - 1250077
ER -