Related papers: Nested open books and the binding sum
We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. The predicted equations are derived in this model, and new equations can be discovered as well.…
We sketch the proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology. The key point is to express these two Floer homology theories in terms of an open book decomposition of the ambient…
In this paper, we obtain some new results on closed subschemes. Specially, we define natural addition and multiplication on the closed subschemes of a scheme. It is shown that "the multiplication" precisely coincides with the well known…
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner…
In earlier work a description of a physical entity is given by means of a state property system and it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between…
The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or…
We propose a generalization of the classical notions of plumbing and Murasugi summing operations to smooth manifolds of arbitrary dimensions, so that in this general context Gabai's credo "the Murasugi sum is a natural geometric operation"…
We examine open books with powers of fibered Dehn twists as monodromy. The resulting contact manifolds can be thought of as Boothby-Wang orbibundles over symplectic orbifolds. Using the mean Euler characteristic of equivariant symplectic…
A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed,…
The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each…
We give a criterion for an open book to contain an n-times iterated Hopf plumbing summand. As an application, we show that fibre surfaces of positive braid knots admit a trefoil plumbing structure.
Let $M$ be a closed, oriented, connected 3--manifold and $(B,\pi)$ an open book decomposition on $M$ with page $\Sigma$ and monodromy $\varphi$. It is easy to see that the first Betti number of $\Sigma$ is bounded below by the number of…
Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.
We use parameterized Morse theory on the pages of an open book decomposition to efficiently encode the contact topology in terms of a labelled graph on a disjoint union of tori (one per binding component). This construction allows us to…
We consider a compact $C^\infty$ stratified 2D variety $M$ in $\mathbb{R}^3$ and its $\epsilon$ neighborhood $M_\epsilon$, which we call a "fattened open book structure". Assuming absence of zero-dimensional strata, i.e. "corners", we show…
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…
Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…
We study structural and topological properties of nested set complexes of matroids with arbitrary building sets, proving that these complexes are vertex decomposable and admit convex ear decompositions. These results unify and generalize…
We associate an open book with any connected plane checkerboard graph, thus providing a common extension of the classes of prime positive braid links and positive tree-like Hopf plumbings. As an application, we prove that the link type of a…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…