arXiv subjects

Jules R. Metcalf-Burton

Publications and source records attributed to Jules R. Metcalf-Burton.

2 recordsLinked to original sources

arXiv2016

Double branched covers of theta-curves

We prove a folklore theorem of W. Thurston which provides necessary and sufficient conditions for primality of a certain class of theta-curves. Namely, a theta-curve in the 3-sphere with an unknotted constituent knot U is prime if and only if lifting the third arc of the theta-curve to the double branched cover over U produces a prime knot. We apply this result to Kinoshita's theta-curve.

math.GT↗

arXiv2012

Borromean rays and hyperplanes

Three disjoint rays in euclidean 3-space 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.

math.GT↗