7 papers
Torus knots as loop-edges in three-sphere triangulations
Lezhi Lin, Jonathan Spreer
We present a procedure that, given a pair of coprime integers, produces a one-vertex triangulation of the three-sphere containing the corresponding torus knot as an edge. The const…
The search for exotic knot traces
Marc Kegel, Jonathan Spreer
Two distinct knots are said to be friends if their complements, filled along the 0-slope, produce diffeomorphic 3-manifolds. In this article, we develop a practical algorithm, impl…
A census of face-transitive surfaces
Reymond Akpanya, Jonathan Spreer
A face-transitive surface is a triangulated 2-dimensional manifold whose automorphism group acts transitively on its set of triangles. In this paper, we investigate this class of h…
Small Triangulations of Simply Connected 4-Manifolds
Jonathan Spreer, Lucy Tobin
We present small triangulations of all connected sums of and with the standard piecewise linear structure. Our triangulations have pentach…
Independence complexes of circle graphs
Rhea Palak Bakshi, Ali Guo, Dionne Ibarra +4
Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link , they reveal topological properties of , more…
Triangulations of the 3-sphere with knotted edge
Dionne Ibarra, Daniel V. Mathews, Jessica S. Purcell +1
We prove that for any knot , there exists a one-vertex triangulation of the -sphere containing an edge forming . The proof is constructive, and based on fully augmented li…
On the complexity of 2-bridge link complements
James Morgan, Jonathan Spreer
We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string br…