J Rubinstein
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Immersed flat ribbon knots Open
We study the minimum ribbonlength for immersed planar ribbon knots and links. Our approach is to embed the space of such knots and links into a larger more tractable space of disk diagrams. When length minimisers in disk diagram space are …
The 3D index and Dehn filling Open
We provide a rigorous proof of the Gang-Yonekura formula describing the transformation of the 3D index under Dehn filling a cusp in an orientable 3-manifold. The 3D index, originally introduced by Dimofte, Gaiotto and Gukov, is a physicall…
BAZ volume 106 issue 2 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
BAZ volume 106 issue 1 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
A new family of minimal ideal triangulations of cusped hyperbolic 3-manifolds Open
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 triangulations of once-punctured torus bundles. This paper exhibit…
A Gradient Descent Method for The Dubins Traveling Salesman Problem Open
We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature-constrained tour through a finite number of points in the …
Immersed flat ribbon knots Open
We study the minimum ribbonlength for immersed planar ribbon knots and links. Our approach is to embed the space of such knots and links into a larger more tractable space of disk diagrams. When length minimisers in disk diagram space are …
Traversing three-manifold triangulations and spines Open
A celebrated result concerning triangulations of a given closed three-manifold is that any two triangulations with the same number of vertices are connected by a sequence of so-called 2–3 and 3–2 moves. A similar result is known for ideal …
Multisections of piecewise linear manifolds Open
Recently Gay and Kirby described a new decomposition of smooth closed $4$-manifolds called a trisection. This paper generalises Heegaard splittings of $3$-manifolds and trisections of $4$-manifolds to all dimensions, using triangulations a…
Generalized trisections in all dimensions Open
Significance Decomposing a manifold into handles was introduced by Smale, from the study of the critical points of smooth real-valued functions. Here we study combinatorial functions from a manifold to a simplex and use them to decompose t…
Computing trisections of 4-manifolds Open
Significance Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way …
Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds Open
In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Hee…
A Geometric approach to shortest bounded curvature paths Open
Consider two elements in the tangent bundle of the Euclidean plane $(x,X),(y,Y)\in T{\mathbb R}^2$. In this work we address the problem of characterizing the paths of bounded curvature and minimal length starting at $x$, finishing at $y$ a…
Computing trisections of 4-manifolds Open
Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to algorithmi…
BAZ volume 95 Issue 2 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
BAZ volume 95 Issue 1 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Triangulations of 3–Manifolds with essential edges Open
We define essential and strongly essential triangulations of –manifolds, and give four constructions using different tools (Heegaard splittings, hierarchies of Haken 3–manifolds, Epstein-Penner decompositions, and cut loci of Riemannian ma…