arXiv research

New series invariant for knots and cables, with robustness and relations.

Study series invariants of plumbed 3-manifolds using root lattices.

Innovative series invariant for knot complements, linking to existing invariants.

Study series invariants for plumbed 3-manifolds and their properties.

Power series invariant of hyperbolic 3-manifolds matches knot invariants.

Researchers calculate $(t,q)$-series invariants for Seifert manifolds.

Researchers confirm a relation between knot invariants and provide formulas for torus knots.

Study compares WRT and CGP invariants using Habiro's series.

Researchers derive $q$-series for $SO(3)$ and $OSp(1|2)$ groups.

New invariant connects knot homology and BPS series for plumbed knot complements.

New cobordism invariants derived from BPS q-series.

Study delta invariant of curves on rational surfaces using topological methods.

Formula connects knot complements' invariants.

In his 1957 paper, John Milnor introduced link invariants which measure the homotopy class of the longitudes of a link relative to the lower central series of the link group. Consequently, these invariants determine the lower central series quotients of the link group. This work has driven decades of research with prof…

New formula and properties of inverted Habiro series derived from GM series.

Paper connects knot invariants and Morse flow loops.

This review connects knot invariants to quiver representations.

New invariant unifies two theories of 3-manifolds, recovering quantum invariants.

We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating fun…

This paper introduces new invariants for time series analysis.

Infinite families of quantum modular invariants for 3-manifolds are discovered.

New connections found between knot invariants and Rozansky-Witten theory.

New Bailey pairs derived for tetrahedron index, linking knot invariants.

We prove Fu's power series conjecture which relates the algebra of isometry invariant valuations on complex space forms to a formal power series from combinatorics which was introduced by Tutte. The $n$-th coefficient of this series is the number of triangulations of a triangle with $3n$ internal edges; or the number o…

Quantum invariants of 3-manifolds and links reviewed, with connections to other topological invariants.

New relation between quantum groups and BPS series.

The paper generalizes BPS-series for $(2,2w+1)$-cabling of figure eight knot.

Paper constructs new identities linking quantum invariants and modular forms.

New invariants for 3-manifolds derived from supergroup representations.

We construct power series invariants of rational homology 3-spheres from quantum PSU(n)-invariants. The power series can be regarded as perturbative invariants corresponding to the contribution of the trivial connection in the hypothetical Witten's integral. This generalizes a result of Ohtsuki (the $n=2$ case) which l…

New curves share invariant up to any fixed order.

The paper characterizes and examines nilpotent complex structures on stratified Lie algebras.

The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in $1/N$. We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power se…

Invariants measure letter interleaving in groups, detecting group dimensions.

Computes link invariants in real projective 3-space using topological vertex.

Study on $Δ$ invariants of plumbed 3-manifolds, comparing with Heegaard-Floer homology.

GT-PCA improves PCA for image and time series data.

Given a time series of graphs G(t) = (V, E(t)), t = 1, 2, ..., where the fixed vertex set V represents "actors" and an edge between vertex u and vertex v at time t (uv \in E(t)) represents the existence of a communications event between actors u and v during the tth time period, we wish to detect anomalies and/or chang…

New q-series found for osp(2|2n) Lie superalgebra.

The physical 3d $\mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $\hat{Z}_{a}(q)$ that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten-Reshetikhin-Turaev invari…

Extends A-type coefficient polynomials to B-type setting, introducing new invariants.

AR model forecasts partially observed dynamical time series by estimating evolution function and imputing missing variables.

A new method extracts features from time series data using iterated sums and improves classification accuracy.

For a Seifert fibered homology sphere we show that the q-series Z-hat invariant introduced by Gukov, Pei, Putrov and Vafa is a resummation of the Ohtsuki serie. We show that for every even level k there exists a full asymptotic expansion of Z-hat for q tending to a certain k'th root of unity and in particular that the …

Recently, researchers have started applying convolutional neural networks (CNNs) with one-dimensional convolutions to clinical tasks involving time-series data. This is due, in part, to their computational efficiency, relative to recurrent neural networks and their ability to efficiently exploit certain temporal invari…

Invariants of hyperbolic knots connect to quantum modularity.

For Poincare series of binary polyhedral groups and Coxeter polynomials there are obtained statements close to the Euclid algorithm and orthogonal polynomials theory: generalized Ebeling formula, decompositions into ramified continued fractions, Christoffel-Darboux identity, combinatorial formula. Known results about t…

The abstract discusses resurgent functions in quantum knot invariants.