Related papers: Strongly invertible knots, rational-fold branched …
A marked strongly invertible knot is a triple $(K,h,\delta)$ of a knot $K$ in $S^3$, a strong inversion $h$ of $K$, and a subarc $\delta \subset \operatorname{Fix}(h)\cong S^1$ bounded by $\operatorname{Fix}(h)\cap K\cong S^0$. An invariant…
We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…
In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of…
We use Dehn surgery methods to construct infinite families of hyperbolic knots in the 3-sphere satisfying a weak form of the Turaev--Viro invariants volume conjecture. The results have applications to a conjecture of Andersen, Masbaum, and…
We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.
We give two constructions of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new…
Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in the fundamental group of M, and that the double cosets for crossing surfaces are also separable. We deduce that if there…
We prove there is a class of maps $\gamma:\mathbb{T}^{2n}\rightarrow\mathbb{S}^1$ such that a conservative dynamically coherent partially hyperbolic skew-product on $\mathbb{T}^{2n}\times\mathbb{S}^1$ with fixed hyperbolic dynamics on the…
Given a scheme over a field endowed with a strict normal crossings divisor, we define strongly parabolic connections, consistently with the current terminology for Higgs bundles. When the weights are rational with prescribed denominators,…
Kang and Park recently showed that every cubic (loopless) multigraph is incidence 6-choosable [On incidence choosability of cubic graphs. \emph{arXiv}, April 2018]. Equivalently, every bipartite graph obtained by subdividing once every edge…
Internal stabilization adds a trivial handle to an embedded surface in a coordinate chart. It is known that any pair of smoothly knotted surfaces in a simply-connected $4$-manifold become smoothly isotopic after sufficiently many internal…
We take a general approach to uncertainty on product spaces, and give sufficient conditions for the independence structures of uncertainty measures to satisfy graphoid properties. Since these conditions are arguably more intuitive than some…
This paper shows that the complex projective plane $\mathbb{P}^2$ can be realized as the underlying space for a closed hyperbolic $4$-orbifold. This is the first example of a closed hyperbolic $4$-orbifold whose underlying space is…
We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction…
Consider a three dimensional partially hyperbolic diffeomorphism. It is proven that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) either an Anosov diffeomorphism, a skew-product…
We develop a simple procedure that allows one to explicitly reconstruct any piecewise linear path from its signature. The construction is based on the development of the path onto the hyperbolic space.
We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit version of the problem. We show that, for example,…
We consider closed orientable 3-dimensional hyperbolic manifolds which are cyclic branched coverings of the 3-sphere, with branching set being a two-bridge knot (or link). We establish two-sided linear bounds depending on the order of the…
Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…