23 citations · 199 across the 45 of their papers we have counts for
50 papers
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…
Simplicial cell decompositions of
Basudeb Datta, Jonathan Spreer
According to a well-known result in geometric topology, we have \linebreak , where $\operatorname{Sym}(…
Sampling triangulations of manifolds using Monte Carlo methods
Eduardo G. Altmann, Jonathan Spreer
We propose a Monte Carlo method to efficiently find, count, and sample abstract triangulations of a given manifold M. The method is based on a biased random walk through all possib…
Hopf triangulations of spheres and equilibrium triangulations of projective spaces
Wolfgang Kühnel, Jonathan Spreer
Following work by the first author and Banchoff, we investigate triangulations of real and complex projective spaces of real and complex dimension that are adapted to the decom…
On the width of complicated JSJ decompositions
Kristóf Huszár, Jonathan Spreer
Motivated by the algorithmic study of 3-dimensional manifolds, we explore the structural relationship between the JSJ decomposition of a given 3-manifold and its triangulations. Bu…
A Uniform Sampling Procedure for Abstract Triangulations of Surfaces
Rajan Shankar, Jonathan Spreer
We present a procedure to sample uniformly from the set of combinatorial isomorphism types of balanced triangulations of surfaces - also known as graph-encoded surfaces. For a give…
Complexity of 3-manifolds obtained by Dehn filling
William Jaco, J. Hyam Rubinstein, Jonathan Spreer +1
Let be a compact 3--manifold with boundary a single torus. We present upper and lower complexity bounds for closed 3--manifolds obtained as even Dehn fillings of As an app…
A new family of minimal ideal triangulations of cusped hyperbolic 3-manifolds
J. Hyam Rubinstein, Jonathan Spreer, Stephan Tillmann
Previous work of the authors with Bus Jaco determined a lower bound on the complexity of cusped hyperbolic 3-manifolds and showed that it is attained by the monodromy ideal triangu…
Slope norm and an algorithm to compute the crosscap number
William Jaco, J. Hyam Rubinstein, Jonathan Spreer +1
We give three algorithms to determine the crosscap number of a knot in the 3-sphere using -efficient triangulations and normal surface theory. Our algorithms are shown to be cor…
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…
Parametrized Complexity of Expansion Height
Ulrich Bauer, Abhishek Rathod, Jonathan Spreer
Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of th…
Combinatorial Inscribability Obstructions for Higher-Dimensional Polytopes
Joseph Doolittle, Jean-Philippe Labbé, Carsten E. M. C. Lange +3
For -dimensional convex polytopes, inscribability is a classical property that is relatively well-understood due to its relation with Delaunay subdivisions of the plane and hype…
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)…
Average Betti numbers of induced subcomplexes in triangulations of manifolds
Giulia Codenotti, Francisco Santos, Jonathan Spreer
We study a variation of Bagchi and Datta's -vector of a simplicial complex , whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of . W…
On minimal ideal triangulations of cusped hyperbolic 3-manifolds
William Jaco, Hyam Rubinstein, Jonathan Spreer +1
Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dime…
Short proof of two cases of Chvátal's conjecture
Jorge Olarte, Francisco Santos, Jonathan Spreer
In 1974 Chvátal conjectured that no intersecting family in a downset can be larger than the largest star. In the same year Kleitman and Magnanti proved the conjecture…
Z2-Thurston Norm and Complexity of 3-Manifolds, II
William Jaco, J. Hyam Rubinstein, Jonathan Spreer +1
In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our…
Determining the trisection genus of orientable and non-orientable PL 4-manifolds through triangulations
Jonathan Spreer, Stephan Tillmann
Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genu…
On the treewidth of triangulated 3-manifolds
Kristóf Huszár, Jonathan Spreer, Uli Wagner
In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, s…
The EKR property for flag pure simplicial complexes without boundary
Jorge Olarte, Francisco Santos, Jonathan Spreer +1
We prove that the family of facets of a pure simplicial complex of dimension up to three satisfies the Erdős-Ko-Rado property whenever it is flag and has no boundary ridges. We con…
Unravelling the Dodecahedral Spaces
Jonathan Spreer, Stephan Tillmann
The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbol…