Related papers: Uniform Convergence and Knot Equivalence

We consider ribbon n-knots for n\geq 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are…

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose…

Uniform random intersection graphs have received much interest and been used in diverse applications. A uniform random intersection graph with $n$ nodes is constructed as follows: each node selects a set of $K_n$ different items uniformly…

We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric…

A fundamental tool in the analysis of Ricci flow is a compactness result of Hamilton in the spirit of the work of Cheeger, Gromov and others. Roughly speaking it allows one to take a sequence of Ricci flows with uniformly bounded curvature…

We prove that if $Y$ is the Gromov-Hausdorff limit of a sequence of compact manifolds, $M^n_i$, with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then $Y$ has a universal cover. We then show that, for $i$…

In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case…

We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant…

Let $\mathcal{L}$ be a knot with a fixed positive crossing and $\mathcal{L}_n$ the link obtained by replacing this crossing with $n$ positive twists. We prove that the knot Floer homology $\widehat{\text{HFK}}(\mathcal{L}_n)$ `stabilizes'…

Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…

We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…

Let K be a knot in a closed orientable irreducible 3-manifold M and let P be a Heegaard splitting of the knot complement of genus at least two. Suppose Q is a bridge surface for K. Then either \begin{itemize} \item $d(P)\leq 2-\chi(Q-K)$,…

We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or…

Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…

Let $(S_1, S_2)$ be a bi-isometry, that is, a pair of commuting isometries $S_1$ and $S_2$ on a complex Hilbert space $\mathscr H.$ By the von Neumann-Wold decomposition, the hyper-range $\mathscr H_\infty(S_1):=\cap_{n=0}^\infty…

The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function,…

We prove that for some knot-like objects one can easily recognize non-equivalence w.r.t. all Reidemeister moves by studying some equivalence classes modulo only 2nd Reidemeister moves. There are applications to virtual knots, graph-links…

We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These "relative adjunction inequalities" improve the adjunction inequalities for closed surfaces which have been…

Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also…

We determine bubble tree convergence for a sequence of harmonic maps, with uniform energy bounds, from a compact Riemann surface into a compact locally CAT(1) space. In particular, we demonstrate energy quantization and the no-neck property…