arXiv research

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

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

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…

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…

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.

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.

Non-trivial action on surface configuration homology.

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.

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

New construction provides non-trivial representations for geometric quantisation.

Every non-trivial knot group is fully residually perfect.

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

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…

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

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.

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.

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.

We present some non-trivial calculations of Baldwin-Ozsváth-Szabó cohomology of links, and applications to Heegaard-Floer homology of branched double covers.

In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial $Δ_{L}(t)$ is vanishing, then $L$ admits a non-trivial coloring by any non-trivial Alexander quandle $Q$, and that if $Δ_{L}(t)=1$, then $L$ admits only the trivial coloring by any Alexa…

The paper revisits a claim about a principal bundle over a contractible base and finds it non-trivial.

The paper constructs non-trivial cocycles for long embeddings with more than one loop.

For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of Fox colors is p. We also prove that we can assemble a non-trivial p-coloring with any number of colors, from the minimum to the maximum number of colors. Furthermore, for any rational link, we prove …

For n at least 3, let SAut(F_n) denote the unique subgroup of index two in the automorphism group of a free group. The standard linear action of SL(n,Z) on R^n induces non-trivial actions of SAut(F_n) on R^n and on S^{n-1}. We prove that SAut(F_n) admits no non-trivial actions by homeomorphisms on acyclic manifolds or …

Paper detects non-trivial cycles in embedding spaces using graph integrals.

Study the isoperimetric problem in Riemannian manifolds with non-trivial conformal vector fields.

The paper explores idempotents in quandle rings and their connections to quandle coverings.

Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain condi…

Existence of non-trivial monopoles on 3-spheres proven.

We characterize the (1, 1) knots in the three-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non- trivial L-space surgeries. We also recover a characterization of the Berge manifold amongst 1-bridge braid exteriors.

We study comparison formulas for $ζ$-regularized determinants of self-adjoint extensions of the Laplacian on flat conical surfaces of genus $g\geq 2$. The cases of trivial and non-trivial holonomy of the metric turn out to differ significantly.

Cocycles are constructed by polynomial expressions for Alexander quandles. As applications, non-triviality of some quandle homology groups are proved, and quandle cocycle invariants of knots are studied. In particular, for an infinite family of quandles, the non-triviality of quandle homology groups is proved for all o…

The A-polynomial of a knot in S^3 defines a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL(2,C). Here, we show that a non-trivial knot in S^3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU_2-…

We construct explicit examples of Dirac-harmonic maps $(φ, ψ)$ between Riemannian manifolds $(M,g)$ and $(N,g')$ which are non-trivial in the sense that $φ$ is not harmonic. When $\dim M=2$, we also produce examples where $φ$ is harmonic, but not conformal, and $ψ$ is non-trivial.

2-twist trefoil has 6 crossings, proving non-trivial knotted surface.

The paper constructs homotopically non-trivial spheres in complexified spaces.

We show that the distance of a link $K$ with respect to a bridge surface of any genus determines a lower bound on the genus of essential surfaces and Heegaard surfaces in the manifolds that result from non-trivial Dehn surgeries on the knot. In particular, knots with high bridge distance do not admit non-trivial non-hy…

Proves cosmetic crossing conjecture for certain knots.

Non-trivialization probability of arc system in 3D space

New findings on Jones polynomial for 4-strand braids.

Index difference on surfaces of genus at least 3 is non-trivial.