Tootfinder

"... and the darkness takes over"
(Original title: Abyssal)
https://thesecretknots.com/comic/abyssal/

Persistent foliarity of (1,1) almost L-space knots
Qingfeng Lyu
https://arxiv.org/abs/2510.11533 https://arxiv.org/pdf/2510.11533

Persistent foliarity of (1,1) almost L-space knots
We propose a branched surface model that could be used to prove (1,1) non-L-space knots in $S^3$ and lens spaces are persistently foliar. We verify that this model works for (1,1) almost L-space knots.

tonight is garlic knots, absolutely covered in parmesan

$h$-Principles for smooth curves and knots with prescribed curvature
Mohammad Ghomi, Matteo Raffaelli
https://arxiv.org/abs/2510.05275 https://arxiv.org/pd…

$h$-Principles for smooth curves and knots with prescribed curvature
We show that smooth curves with prescribed curvature satisfy a $C^1$-dense $h$-principle in the space of immersed curves in Euclidean space. More precisely, every $C^{α\geq 2}$ curve with nonvanishing curvature in $R^{n\geq 3}$ can be $C^1$-approximated by $C^α$ curves of any larger curvature, prescribed as a function of arclength. It follows that there exist $C^\infty$ knots of prescribed curvature in every isotopy class of closed curves embedded in $R^3$.

*Me staring at a pair of leggings with elaborate Celtic knotwork on the thighs and calves and wanting*
My brain: “you know this is a scam, right? That would take hours and hours of work on the part of a costumer, like how you used to be? And they’re $30‽ c’mon!”
Me: “shut up brain”

Non-decomposable Lagrangian cobordisms between Legendrian knots
Roman Golovko, Daniel Kom\'arek
https://arxiv.org/abs/2511.08731 https://arxiv.org/pdf/2511.08731 https://arxiv.org/html/2511.08731
arXiv:2511.08731v1 Announce Type: new
Abstract: For a given $g>0$, we construct the family of non-decomposable Lagrangian cobordisms of genus $g$ between (stabilized) Legendrian knots in the standard contact three-sphere. The main method to obstruct decomposability that we use is the application of the Livingston's estimates.
toXiv_bot_toot

On asymmetric hyperbolic L-space knots of braid index four
Kenneth L. Baker, Masakazu Teragaito
https://arxiv.org/abs/2510.07618 https://arxiv.org/pdf/2510…

On asymmetric hyperbolic L-space knots of braid index four
A knot is called an L-space knot if it admits a positive Dehn surgery yielding an L-space. In the SnapPy census, there are exactly 9 asymmetric L-space knots. Among them, the knot t12533 is the only known example of braid index 4. We generalize this knot, and give the first infinite family of asymmetric hyperbolic L-space knots of braid index 4.

The first proper motion measurement of the acceleration regions in the large-scale jets of SS 433 powering the W50 nebula
Naomi Tsuji, Yoshiyuki Inoue, Dmitry Khangulyan, Kaya Mori, Samar Safi-Harb, Takaaki Tanaka, Laura Olivera-Nieto, Brydyn Mac Intyre, Kazuho Kayama, Takeshi Go Tsuru, Hiroyuki Uchida, Tatsuki Fujiwara, Felix Aharonian
https://

The first proper motion measurement of the acceleration regions in the large-scale jets of SS 433 powering the W50 nebula
We report on new Chandra ACIS-I observations of the X-ray knots located in the western and eastern lobes of W50 associated with the parsec-scale jets of the Galactic microquasar SS 433. These knots are likely counterparts of the recently detected very-high-energy ($E>100$ GeV) gamma-ray emission by HAWC and H.E.S.S. These findings, together with the ultra-high-energy signal recently reported by the LHAASO collaboration, have established the SS 433/W50 system as a unique jet-driven PeVatron cand…

🇺🇦 #NowPlaying on KEXP's #DriveTime
Cults:
🎵 Knots
#Cults
https://open.spotify.com/track/2N07aFwOw7gt6cg5awcNx4

Eagles vs. Broncos takeaways: Bo Nix, Denver hand Philadelphia its first loss https://www.nytimes.com/athletic/6691825/2025/10/05/broncos-eagles-score-result-takeaways-nfl/

Constructing and Cataloging 2-Adjacent Knots
John Carney, Everett Meike
https://arxiv.org/abs/2510.00291 https://arxiv.org/pdf/2510.00291

Constructing and Cataloging 2-Adjacent Knots
Generalizing unknotting number, $n$-adjacent knots have $n$ crossings such that changing any non-empty subset of them results in the unknot. In this paper, we determine the 2-adjacent knots through 12 crossings. Using Heegaard Floer $d$-invariants and the Alexander polynomial, we develop a new technique to obstruct 2-adjacency, and we prove conjectures of Ito and Kato regarding 2-adjacent knots.

A stud of 2-periodic weft-knitted textiles using the theory of knots and links
Miriam Kuzbary, Shashank G. Markande, Elisabetta A. Matsumoto, Stanley Pritchard
https://arxiv.org/abs/2510.08384

A stud of 2-periodic weft-knitted textiles using the theory of knots and links
In this study, we use a correspondence between two-periodic weft-knitted textiles and links in the thickened torus to study the former using link invariants. We establish a criterion to identify the set of links whose elements are realized through techniques of weft-knitting leading to new, unconventional types of weft-knitting stitch patterns. A crucial topological underpinning of these links is shown to be their correspondence with ribbon knots and links in Euclidean three-space and equivalen…

Embedding calculus and Vassiliev spectral sequence
Syunji Moriya
https://arxiv.org/abs/2509.23766 https://arxiv.org/pdf/2509.23766

Embedding calculus and Vassiliev spectral sequence
Vassiliev spectral sequence and Sinha spectral sequence are both related to cohomology of the space of long knots $\mathbb{R}\to \mathbb{R}^3$. Although they have different origins, the Vassiliev $E_1$-page and the Sinha $E_2$-page are isomorphic (up to a degree shift). In this paper, we prove that they have isomorphic $E_\infty$-pages if the coefficient ring is a field. Together with degeneracy of the Sinha sequence, this implies that the Vassiliev sequence degenerates at $E_1$-page over $\mat…

Structure groups and second homology groups of linear Alexander quandles
Adrien Cl\'ement
https://arxiv.org/abs/2510.00830 https://arxiv.org/pdf/2510.0…

Structure groups and second homology groups of linear Alexander quandles
Quandles are self-distributive algebraic structures known as sources of strong knots invariants, but also appearing in other contexts. From any quandle, one can construct two invariants: the structure group and the second quandle homology group. These groups are useful in applications, but hard to compute. In this paper, we focus on Alexander quandles over a cyclic group $\mathbb{Z}_n$. By using explicit rewriting techniques, we show that the structure group of such a quandle injects into $\mat…

Crosslisted article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- Affine representations of rational and pretzel knots
Javier Mart\'inez

Quasi-alternating surgeries on asymmetric L-space knots in the census
Masakazu Teragaito
https://arxiv.org/abs/2510.04403 https://arxiv.org/pdf/2510.04403

Quasi-alternating surgeries on asymmetric L-space knots in the census
In the SnapPy census, there are 9 asymmetric L-space knots. It is known that each of them admits exactly two quasi-alternating surgeries with the aid of a computer. The purpose of this article is to confirm these surgeries by the Montesinos trick.

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Non-decomposable Lagrangian cobordisms between Legendrian knots
Roman Golovko, Daniel Kom\'arek
https://arxiv.org/abs/2511.08731 https://mastoxiv.page/@arXiv_mathSG_bot/115541377678336506
- Spaces of Legendrian cables and Seifert fibered links
Eduardo Fern\'andez, Hyunki Min
https://arxiv.org/abs/2310.12385 https://mastoxiv.page/@arXiv_mathGT_bot/111265563434686287
- Almost Hermitian structures on virtual moduli spaces of non-Abelian monopoles and applications to...
Paul M. N. Feehan, Thomas G. Leness
https://arxiv.org/abs/2410.13809 https://mastoxiv.page/@arXiv_mathDG_bot/113327305560976416
- Quantum cohomology, shift operators, and Coulomb branches
Ki Fung Chan, Kwokwai Chan, Chin Hang Eddie Lam
https://arxiv.org/abs/2505.23340 https://mastoxiv.page/@arXiv_mathAG_bot/114595582234065991
- One application of Duistermaat-Heckman measure in quantum information theory
Lin Zhang, Xiaohan Jiang, Bing Xie
https://arxiv.org/abs/2507.02369 https://mastoxiv.page/@arXiv_quantph_bot/114794376818737255
toXiv_bot_toot

Knots and variance ordering of sequential Monte Carlo algorithms
Joshua J Bon, Anthony Lee
https://arxiv.org/abs/2510.01901 https://arxiv.org/pdf/2510.0190…

Knots and variance ordering of sequential Monte Carlo algorithms
Sequential Monte Carlo algorithms, or particle filters, are widely used for approximating intractable integrals, particularly those arising in Bayesian inference and state-space models. We introduce a new variance reduction technique, the knot operator, which improves the efficiency of particle filters by incorporating potential function information into part, or all, of a transition kernel. The knot operator induces a partial ordering of Feynman-Kac models that implies an order on the asymptot…

Non-Simple knots in Contact 3-Manifolds
Ipsita Datta, Tanushree Shah
https://arxiv.org/abs/2510.02932 https://arxiv.org/pdf/2510.02932

Non-Simple knots in Contact 3-Manifolds
We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is rich. In fact, there are more non-isotopic Legendrians that are topologically isotopic to the $n$-twist knot in a Lens space $L(α, β)$ than in $S^3$. We also include connect sum formulas for rational variants of classical invariants, $\mathrm{tb}_\mathbb{Q}$, $\mathrm{rot}_\mathbb{Q}$, and $\mathrm{sl}_\mathbb{Q}$, whi…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Sinha's spectral sequence for long knots in codimension one and non-formality of the little 2-dis...
Syunji Moriya

Extrinsic systole of Seifert surfaces and distortion of knots
Sahana Vasudevan
https://arxiv.org/abs/2510.01095 https://arxiv.org/pdf/2510.01095

Extrinsic systole of Seifert surfaces and distortion of knots
In 1983, Gromov introduced the notion of distortion of a knot, and asked if there are knots with arbitrarily large distortion. In 2011, Pardon proved that the distortion of $T_{p,q}$ is at least $\min\{p,q\}$ up to a constant factor. We prove that the distortion of $T_{p, p+1}\# K$ is at least $p$ up to a constant, independent of $K$. We also prove that any embedding of a minimal genus Seifert surface for $T_{p,p+1}\# K$ in $\mathbb{R}^3$ has small extrinsic systole, in the sense that it contai…

Surgeries on knots and tight contact structures
Zhenkun Li, Shunyu Wan, Hugo Zhou
https://arxiv.org/abs/2510.05294 https://arxiv.org/pdf/2510.05294

Surgeries on knots and tight contact structures
For any knot $K$ in $S^3$ and any positive rational $r$, we show that smooth $(-r)$-surgery on $K$ always admits a tight contact structure. More specifically, the tightness is detected by the non-vanishing Heegaard Floer contact invariant.

Affine representations of rational and pretzel knots
Javier Mart\'inez
https://arxiv.org/abs/2510.02077 https://arxiv.org/pdf/2510.02077

Affine representations of rational and pretzel knots
We construct and study representations of rational and pretzel tangle and knot groups into the affine group $\mathrm{AGL}(1,\mathbb{C})$, via a TQFT that is valued in the category of spans of singular vector bundles over $\mathbb{C}^{\ast}$. For these families, we derive closed-form expressions for their Alexander polynomials and establish bounds on their zeros. Finally, we specialize the functor at $t=-1$ and analyze colorings of rational tangles in terms of spans of complex vector spaces.

Exact integral formulas for volumes of two-bridge knot cone-manifolds
Anh T. Tran, Nisha Yadav
https://arxiv.org/abs/2510.02095 https://arxiv.org/pdf/2510.…

Exact integral formulas for volumes of two-bridge knot cone-manifolds
We provide exact integral formulas for hyperbolic and spherical volumes of cone-manifolds whose underlying space is the $3$-sphere and whose singular set belongs to three infinite families of two-bridge knots: $C(2n,2)$ (twist knots), $C(2n,3)$, and $C(2n,-2n)$ for any non-zero integer $n$. Our formulas express volumes as integrals of explicit rational functions involving Chebyshev polynomials of the second kind, with integration limits determined by roots of algebraic equations. This extends p…

Non-characterizing slopes for more 3-manifolds
Matthew Elpers
https://arxiv.org/abs/2510.05412 https://arxiv.org/pdf/2510.05412

Non-characterizing slopes for more 3-manifolds
For any homotopy class h in any compact orientable 3-manifold M which is closed or has exclusively torus boundary components, we produce infinitely many pairs of distinct knots representing h with orientation-preserving homeomorphic 0-surgeries.

Crosslisted article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- $h$-Principles for smooth curves and knots with prescribed curvature
Mohammad Ghomi, Matteo Raffaelli

Trisected Rainbows and Braids
Rom\'an Aranda, Scott Carter, Julia Courtney, Puttipong Pongtanapaisan
https://arxiv.org/abs/2510.04248 https://arxiv.org…

Trisected Rainbows and Braids
New explicit procedures for passing among triplane diagrams, braid movies, and braid charts for knotted surfaces in $\mathbb{R}^4$ are presented. To this end, rainbow diagrams, which lie between braid charts and triplanes, are introduced. Inequalities relating the braid index and the bridge index of 2-knots are obtained via these procedures. Another consequence is a 4-dimensional version of the classical result that ``the minimal number of Seifert circles equals the braid index of a link'' due …

Ribbon concordance and fibered predecessors
John A. Baldwin, Steven Sivek
https://arxiv.org/abs/2510.02214 https://arxiv.org/pdf/2510.02214

Ribbon concordance and fibered predecessors
Given any knot K in the 3-sphere, we prove that there are only finitely many hyperbolic fibered knots which are ribbon concordant to K. It follows that every fibered knot in the 3-sphere has only finitely many hyperbolic predecessors under ribbon concordance. Our proof combines results about maps on Floer homology induced by ribbon cobordisms with a relationship between the knot Floer homology of a fibered knot and fixed points of its monodromy. We then use the same techniques in combination wi…

Inverted Habiro Series and its Residues
Josef Svoboda
https://arxiv.org/abs/2509.22610 https://arxiv.org/pdf/2509.22610

Inverted Habiro Series and its Residues
We study the Gukov--Manolescu (GM) series of knots and the inverted Habiro series (IHS) proposed by S. Park. We give a new formula for IHS in terms of coefficients of the GM series and truncated theta functions. We prove a multiplication formula for IHS, constructing a natural ring, in analogy with work of Habiro. We study the residues of IHS and apply them to Dehn surgery formulas. We also give a curious relation between the asymptotics of the GM series at roots of unity and the Kashaev invari…

Satellite Operations and $\theta$
Rob McConkey, Luke J Seaton
https://arxiv.org/abs/2509.22939 https://arxiv.org/pdf/2509.22939

Satellite Operations and $θ$
We study the behavior of the knot invariant $θ$ under satellite operations. First, we prove that $θ$ is additive under connected sum. We then introduce a computational tool to generate $t$-twisted Whitehead doubles and apply it to explore the case of untwisted Whitehead doubles. We propose a conjecture describing the behavior of $θ$ on untwisted Whitehead doubles and verify the conjecture for the first 2977 prime knots. The pair of invariants $Θ= (Δ,θ)$ was introduced by Bar-Natan and van…