A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New formula and properties of inverted Habiro series derived from GM series.
New formulas connect knot invariants with theta functions.
The study connects knot complements to 3d theories via half-index calculations.
Proves resurgence properties for Habiro elements from radial limits of theta series.
Given a rational homology 3-sphere M with the first integral homology of rank b and a link L inside M, colored by odd numbers, we construct a unified invariant I_{M,L} belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev…
Study compares WRT and CGP invariants using Habiro's series.
Researchers map knot complements using 3d theories and half-index calculations.
The Habiro ring of a number field uses power series to study algebraic K-theory.
We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl_2 invariants of integral homology 3-spheres. Habiro originally derived these formulas using the quantum group U_q sl_2. As an application, we give a formula for the colored Jones polynomial of twist knots, g…
Researchers lift knot coloring polynomial to Habiro ring.
We give a self-contained treatment of Le and Habiro's approach to the Jones function of a knot and Habiro's cyclotomic form of the Ohtsuki invariant for manifolds obtained by surgery around a knot. On the way we reproduce a state sum formula of Garoufalidis and Le for the colored Jones function of a knot. As a corollar…
Invariants of hyperbolic knots connect to quantum modularity.
Hikami observed a discontinuity in a WRT invariant at roots of unity.
For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower central series of the Torelli group of a surface. In this paper, we observe that t…
AIKAE enhances IKAE for long-term time series forecasting.
New presentation of Goussarov-Habiro Lie algebra using primitive Feynman diagrams.
Defines map from skein module to Habiro ring for quantum modularity.
Paper shows how SFA fits into FBM framework for time series separation.
Constructs explicit nontrivial cycles in Habiro cohomology of smooth varieties.
ProFITi model forecasts irregular time series with missing values using conditional flows.
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure t…
We prove that two closed oriented 3-manifolds have isomorphic quintuplets (homology, space of spin structures, linking pairing, cohomology rings, Rochlin function) if, and only if, they belong to the same class of a certain surgery equivalence relation introduced by Goussarov and Habiro.
In 2006 Habiro initiated a construction of generating functions for Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Buehler and Christian Blanchet we extended his construction to a larger class of 3-manifolds. The unified invariants provide a stron…
We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…
Method generates time-series attribution maps with identifiability guarantees.
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical optimization. Through a computational study involving a stochastic version of a well …
Paper constructs new identities linking quantum invariants and modular forms.
The results become part of an upcoming paper.
The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl_2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra U_h(sl_2) of the Li…
We study the Goussarov-Habiro finite type invariants theory for framed string links in homology balls. Their degree 1 invariants are computed: they are given by Milnor's triple linking numbers, the mod 2 reduction of the Sato-Levine invariant, Arf and Rochlin's invariant. These invariants are seen to be naturally r…
We consider a homological enlargement of the mapping class group, defined by homology cylinders over a closed oriented surface (up to homology cobordism). These are important model objects in the recent Goussarov-Habiro theory of finite-type invariants of 3-manifolds. We study the structure of this group from several d…
In this short note we prove that the Farrell-Jones Fibered Isomorphism Conjecture in L-theory, after inverting 2, is true for a group whose some derived subgroup is free.
Complete classification of links up to specific moves.
New geometric invariant from disc intersections captures all coloured Jones polynomials.
Flow-based deep generative models learn data distributions by transforming a simple base distribution into a complex distribution via a set of invertible transformations. Due to the invertibility, such models can score unseen data samples by computing their exact likelihood under the learned distribution. This makes fl…
New copula models capture volatility and directionality in financial time series.
Proposes iVDFM for identifying latent factors in multivariate time series.
We show that the Artin representation on concordance classes of string links induces a well-defined epimorphism modulo order n twisted Whitney tower concordance, and that the kernel of this map is generated by band sums of iterated Bing-doubles of any string knot with nonzero Arf invariant. We also continue J. Levine's…
K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of -move. In this paper we give another geometric condition in terms of Brunnian local move. The proof is simple and self-contained.
L. Kauffman conjectured that a particular solution of the Chinese Rings puzzle is the simplest possible. We prove his conjecture by using low-dimensional topology and group theory. We notice also a surprising connection between the Chinese Rings and Habiro moves (related to Vassiliev invariants).
A formula for the difference of Vassiliev invariants of degree k+1 of two knots all of whose Vassiliev invariants of degree k agree is proven. The proof uses K. Habiro's C-moves and his theorem which relates them to Vassiliev invariants.
In 1993 K. Habiro defined -move of oriented links and around 1994 he proved that two oriented knots are transformed into each other by -moves if and only if they have the same Vassiliev invariants of order . In this paper we define Vassiliev invariant of type , and show that, for $k=k…
We develop a calculus for diagrams of knotted objects. We define Arrow presentations, which encode the crossing informations of a diagram into arrows in a way somewhat similar to Gauss diagrams, and more generally w-tree presentations, which can be seen as `higher order Gauss diagrams'. This Arrow calculus is used to d…
The Jones polynomial of a knot in 3-space is a Laurent polynomial in , with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing defin…
The -equivalence is an equivalence relation generated by -moves defined by Habiro. Habiro showed that the set of -equivalence classes of the knots forms an abelian group under the connected sum and it can be classified by the additive Vassiliev invariant of order . We see that the set of -…
We present a simple algorithm to forecast vector time series, that is robust against missing data, in both training and inference. It models seasonal annual, weekly, and daily baselines, and a Gaussian process for the seasonally-adjusted residuals. We develop a custom truncated eigendecomposition to fit a low-rank plus…
We present an alternative definition for the Goussarov--Habiro filtration of the Z-module freely generated by oriented integral homology 3-spheres, by means of Lagrangian-preserving homology handlebody replacements (LP-surgeries). Garoufalidis, Goussarov and Polyak proved that the graded space (G_n)_n associated to thi…