7 papers · 1 filter
Triangulating Spun 2-Knot Complements
Rhuaidi Antonio Burke, Benjamin Burton, Arunima Ray +3
A -knot is an embedding of a -sphere into the -sphere. Similar to the case of embedding circles into the -sphere, this allows the -sphere to be knotted. In this shor…
Small Triangulations of -Manifolds: Introducing the -Manifold Census
Rhuaidi Antonio Burke, Benjamin A. Burton, Jonathan Spreer
We present a framework to classify PL-types of large censuses of triangulated -manifolds, which we use to classify the PL-types of all triangulated -manifolds with up to six…
On a volume invariant of 3-manifolds
Marc Kegel, Arunima Ray, Jonathan Spreer +2
This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complemen…
Vertex Bounds in Triangulated -Manifolds and an Application to 4-Manifold Complexity
Jonathan Spreer, Lucy Tobin
We investigate face numbers of generalised triangulations of manifolds in arbitrary dimensions. This is motivated by the study of connections between the combinatorics of triangula…
Hard Diagrams of the Unknot
Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler +5
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in…
3-Manifold triangulations with small treewidth
Kristóf Huszár, Jonathan Spreer
Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth of a compact, connected 3-manifold defined by \[ \operatorname{tw}(M)…