21 citations · 21 across the 2 of their papers we have counts for
5 papers · 1 filter
Prime theta-curves on minimal genus Seifert surfaces
Jack S. Calcut, Jamie Phillips-Freedman
We prove that each prime knot union an essential arc on a minimal genus Seifert surface is a prime theta-curve.
Structure and classification of torus theta-curves
Jack S. Calcut, Samantha E. Nieman
We study theta-curves embedded in a standard torus in the 3-sphere. We show that each nontrivial torus knot together with an essential arc determines a prime theta-curve, yielding…
Artin presentations, triangle groups, and 4-manifolds
Jack S. Calcut, Jun Li
Gonz{á}lez-Acu{ñ}a showed that Artin presentations characterize closed, orientable -manifold groups. Winkelnkemper later discovered that each Artin presentation determines a smo…
Borromean rays and hyperplanes
Jack S. Calcut, Jules R. Metcalf-Burton, Taylor J. Richard +1
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 Borrome…
Connected sum at infinity and Cantrell-Stallings hyperplane unknotting
Jack S. Calcut, Henry C. King, Laurent C. Siebenmann
We give a general treatment of the somewhat unfamiliar operation on manifolds called Connected Sum at Infinity, or CSI for short. A driving ambition has been to make the geometry b…