21 citations · 39 across the 14 of their papers we have counts for
18 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…
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…
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…
The end sum of surfaces
Liam K. Axon, Jack S. Calcut
End sum is a natural operation for combining two noncompact manifolds and has been used to construct various manifolds with interesting properties. The uniqueness of end sum has be…
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…