arXiv research

New formalism solves kinematical constraints in curved backgrounds and non-trivial states.

The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this example is shown to be distinct from the same sphere with the reversed orientation. To demonstrate this fact a state-sum invariant for classical knots and knotted surfaces is developed via a cohomology theory of racks a…

This paper is a survey of several papers in quandle homology theory and cocycle knot invariants that have been published recently. Here we describe cocycle knot invariants that are defined in a state-sum form, quandle homology, and methods of constructing non-trivial cohomology classes.

Generalizes embedding formalism for CFTs on curved backgrounds.

Study shows non-trivial homology classes in certain symmetric manifolds.

New pseudo-Hermitian models from non-semisimple TQFTs.

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a…

The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework f…

Surveying methods to create spaces with non-trivial self covers.

Study shows non-trivial knot Floer homology for specific knots.

New framework shows $C^*$-simplicity for groups without certain subalgebras.

This paper studies quandles with one non-trivial column and their properties.

We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…

Lower bounds of betti numbers for homology groups of racks and quandles will be given using the quotient homomorphism to the orbit quandles. Exact sequences relating various types of homology groups are analyzed. Geometric methods of proving non-triviality of cohomology groups are also given, using virtual knots. The r…

We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of the graph contains a non-splittable 2-component link. We also show that there exis…

The paper proves a generalized Kauffman-Harary conjecture for prime determinant links.

This paper deals with the enumeration of the higher order non-trivial compositions of the differential operations and the directional derivative in the space $R^n$ ($n \geq 3$). We present the recurrences for a counting the higher order non-trivial compositions.

In this note we extend to non trivial Hamiltonian fibrations over symplectically uniruled manifolds a result of Lu's, \cite{Lu}, stating that any trivial symplectic product of two closed symplectic manifolds with one of them being symplectically uniruled verifies the Weinstein Conjecture for closed separating hypersurf…

New knots found with non-trivial Steenrod operations on Khovanov homology.

The paper explores non-trivial welded knots and ribbon torus-knots, proving their existence.

Characterizes G2-structures on Lie algebras with non-trivial center.

Non-trivial conservation law found for a specific system.

In this paper we introduce a new invariant of virtual knots and links that is non-trivial for infinitely many virtuals, but is trivial on classical knots and links. The invariant is initially be expressed in terms of a relative of the bracket polynomial and then extracted from this polynomial in terms of its exponents,…

Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however, focus on a priori state aggregation based on similarities in transition rates, whi…

Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.

Gerbes encode spectral gaps in topological insulators.

We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot homology groups and suggests that they can be interpreted directly in topological st…

Non-trivial action on surface configuration homology.

We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-defi…

We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.

New proof for knot state-sum formula using bijection between states.

We construct a 2-generated 2-related group without non-trivial finite factors. That answers a question of J. Button.

Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_θ$ of the noncommutative torus. We show that such $A_θ$-modules have a natural interpretatio…

New construction provides non-trivial representations for geometric quantisation.

Every non-trivial knot group is fully residually perfect.

New families of embeddings in 4-manifolds, topologically trivial but smoothly non-trivial.

This article addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide new methods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main result in this article i…

We show an integrality of the quantum SU(2)-invariant associated with a non-trivial first cohomology class modulo two.

The study finds non-trivial elements in moduli spaces of curvature metrics.

The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.

The Kauffman-Harary conjecture states that for any reduced alternating diagram K of a knot with a prime determinant p, every non-trivial Fox p-coloring of K assigns different colors to its arcs. We generalize the conjecture by stating it in terms of homology of the double cover of S^3 branched along a link. In this way…

Let X be a compact Kahler manifold with a non-trivial holomorphic Poisson structure. Then there exist deformations of non-trivial generalized Kahler structures with one pure spinor on X. We prove that every Poisson submanifold of X is a generalized Kahler submanifold with respect to the deformed generalized Kahler stru…

We prove that if a link admits non-trivial (2k+1)-colorings, with prime 2k+1>7, it also admits non-trivial (2k+1)-colorings not involving colors 2k, 2k-1, nor k.

By 2-twist-spinning the knotted graph that represents the knotted handlebody $5_2$, we obtain a knotted foam in 4-dimensional space with a non-trivial quandle cocycle invariant.

Abstract: Proves no non-trivial normal orbits for specific Hamiltonians.

The study bounds exceptional surgeries for hyperbolic knots.

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.

GWIL uses Gromov-Wasserstein distance to align expert and imitation agent states.