Related papers: Asymptotic Rasmussen Invariant
M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid…
We present an asymptotic theory for solving the dynamics of slender autophoretic loops and knots. Our formulation is valid for non-intersecting 3D centrelines, with arbitrary chemical patterning and varying (circular) cross-sectional…
We extend Howie's characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary and sufficient conditions for a knot to be toroidally…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
Obtaining a closed-form expression for the colored HOMFLY-PT polynomials of knots from $3$-strand braids carrying arbitrary $SU(N)$ representation is a challenging problem. In this paper, we confine our interest to twisted generalized…
Using the Gordon-Litherland pairing, one can define invariants (signature, nullity, determinant) for ${\mathbb Z}/2$ null-homologous links in thickened surfaces. In this paper, we study the concordance properties of these invariants. For…
We investigate the Reshetikhin--Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double…
We have previously proposed that asymptotically AdS 3D wormholes and black holes can be analytically continued to the Euclidean signature. The analytic continuation procedure was described for non-rotating spacetimes, for which a plane t=0…
The aim of this work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. In particular we will study the asymptotic growth of the Betti numbers of the lattices renormalized by the…
We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of information on the asymptotic geometry of these spaces: in…
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…
In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…
We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological…
We define an invariant ${\varphi}$ for knots in the 3-sphere by means of Donaldson invariants and Floer's instanton homology. Some basic properties of this invariant are established and it is shown that ${\varphi}$ coincides with a special…
We present a comprehensive discussion of gravitational charges and radiation in four-dimensional asymptotically locally de Sitter (AldS) spacetimes. Such spacetimes have compact spatial sections and possess spacelike past and future…
This paper presents three non-linear observers on three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This…
We introduce a new algebraic topological technique to detect non-fibred knots in the three sphere using the twisted Alexander invariants. As an application, we show that for any Seifert matrix of a knot with a nontrivial Alexander…
After motivating the relevance of the Bondi-Metzner-Sachs (BMS) group over the last decades, we review how concepts such as Penrose diagrams and the covariant phase space formalism can be used to understand the asymptotic structure of…
In this paper we construct new invariants of knotoids including the odd writhe, the parity bracket polynomial, the affine index polynomial and the arrow polynomial, and give an introduction to the theory of virtual knotoids. The invariants…
This paper explores a particular statistical model on 6-valent graphs with special properties which turns out to be invariant with respect to certain Roseman moves if the graph is the singular point graph of a diagram of a 2-knot. The…