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articleNo Access
UNCOUNTABLY MANY ARCS IN S³ WHOSE COMPLEMENTS HAVE NON-ISOMORPHIC, INDECOMPOSABLE FUNDAMENTAL GROUPS
- ROBERT MYERS
Journal of Knot Theory and Its Ramifications01 Jun 2000
Preview Abstract
An uncountable collection of arcs in S³ is constructed, each member of which is wild precisely at its endpoints, such that the fundamental groups of their complements are non-trivial, pairwise non-isomorphic, and indecomposable with respect to free products. The fundamental group of the complement of a certain Fox-Artin arc is also shown to be indecomposable.
articleNo Access
Borromean rays and hyperplanes
Journal of Knot Theory and Its Ramifications01 Apr 2014
Preview Abstract
Three disjoint rays in ℝ³ form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.