16 citations · 28 across the 10 of their papers we have counts for
13 papers
On the nonorientable 4-genus of double twist knots
Jim Hoste, Patrick D. Shanahan, Cornelia A. Van Cott
We investigate the nonorientable 4-genus of a special family of 2-bridge knots, the twist knots and double twist knots . Because the nonorientable 4-genus is bounded…
Crosscap number and epimorphisms of two-bridge knot groups
Jim Hoste, Patrick D. Shanahan, Cornelia A. Van Cott
We consider the relationship between the crosscap number of knots and a partial order on the set of all prime knots, which is defined as follows. For two knots and , we…
Remarks on Suzuki's Knot Epimorphism Number
Jim Hoste, Joshua Ocana Mercado, Patrick D. Shanahan
A partial order on prime knots can be defined by declaring if there exists an epimorphism from the knot group of onto the knot group of . Suppose that is a 2-br…
Finite -quandles of torus and two-bridge links
Alissa S. Crans, Jim Hoste, Blake Mellor +1
We compute Cayley graphs and automorphism groups for all finite -quandles of two-bridge and torus knots and links, as well as torus links with an axis.
An enumeration process for racks
Jim Hoste, Patrick D. Shanahan
Given a presentation for a rack , we define a process which systematically enumerates the elements of . The process is modeled on the systematic enumeration…
Links with finite -quandles
Jim Hoste, Patrick D. Shanahan
We prove a conjecture of Przytycki which asserts that the -quandle of a link in the 3-sphere is finite if and only if the fundamental group of the -fold cyclic branched c…