4 papers
Mazur's knot and the Octahedron
Jack S. Calcut, Yangyang Du
Mazur's knot exterior admits a geometric description using a single regular ideal octahedron. The resulting hyperbolic structure is closely related to the Whitehead link exterior t…
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…
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.
Ends and end cohomology
William G. Bass, Jack S. Calcut
Ends and end cohomology are powerful invariants for the study of noncompact spaces. We present a self-contained exposition of the topological theory of ends and prove novel extensi…