Tootfinder

Conjugacy invariants for powers of rigid braids: a uniformity phenomenon
Matthieu Calvez (IRISIB), Juan Gonz\'alez-Meneses (DALG-US), Bert Wiest (IRMAR)
https://arxiv.org/abs/2509.01361

Conjugacy invariants for powers of rigid braids: a uniformity phenomenon
Consider an $m$-strand braid $x$ which is rigid in the sense of Garside-theory. Let $SC(x)$ be the set of rigid conjugates of $x$ -- this is a well-known characteristic subset of the conjugacy class of $x$. We present computational evidence that the sequence $(|SC(x^n)|)\_{n\in\mathbb N}$ is not only bounded, but in fact periodic, and that the length of the period can be bounded in terms of the number of strands $m$. We prove this result in the special case of the 3-strand braid group…

A quantization of the $\operatorname{SL}_2(\mathbb{C})$-Chern-Simons invariant of tangle exteriors
Calvin McPhail-Snyder
https://arxiv.org/abs/2509.02365 https://

A quantization of the $\operatorname{SL}_2(\mathbb{C})$-Chern-Simons invariant of tangle exteriors
Previous work of the author and Reshetikhin shows how to use modules over the unrestricted quantum group (at a root of unity) to define quantum representations of a groupoid of braids with flat $\mathfrak{sl}_{2}$ connections on their complements, equivalently $\operatorname{SL}_{2}(\mathbb{C})$ representations or hyperbolic structures. In this article we explain how to use these representations to define quantum invariants $\mathcal{Z}_{N}$ of tangles and links with such geometric structures. …

Cyclic $\mathcal{U}_\xi(\mathfrak{sl}_2)$-modules and invariants of knots with flat $\mathfrak{sl}_2$ connections in the complement
Calvin McPhail-Snyder, Nicolai Reshetikhin
https://arxiv.org/abs/2509.02354

Cyclic $\mathcal{U}_ξ(\mathfrak{sl}_2)$-modules and invariants of knots with flat $\mathfrak{sl}_2$ connections in the complement
The main result of this paper is the factorization of the holonomy $R$-matrix for quantum $\mathfrak{sl}_2$ at a root of unity into a product of four quantum holonomy dilogarithms. This factorization extends previously known results in this direction. We collect many existing results needed for the factorization. We use the holonomy $R$-matrices to define representations of a groupoid of braids with flat $\mathfrak{sl}_{2}$ connections, which also define invariants of knots with such connection…

Earlier today I took a break form work and came out of the office, only to find my wife in full Braids, Cabal Minion cosplay in the living room.
Still kinda weirded-out. She's not _that_ into M:tG, so from my perspective it truly came out of left field. But it also kinda looks good on her, which says what about me exactly?

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Hamiltonian Braids via Generating Functions
Francesco Morabito
https://

Canonical Reduction Systems in Artin-Tits groups of spherical type
Mar\'ia Cumplido, Juan Gonz\'alez-Meneses, Davide Perego
https://arxiv.org/abs/2510.00713 https://

Canonical Reduction Systems in Artin-Tits groups of spherical type
We introduce the canonical reduction system of an element in an Artin-Tits group of spherical type, which generalizes the similar notion for braids (and mapping classes) introduced by Birman, Lubotzky and McCarthy. We show its basic properties, which coincide with those satisfied in braid groups, and we provide an algorithm to compute it. We improve the algorithm in the case of braid groups, and discuss its complexity in this case. As a necessary result for obtaining the general algorithm, we p…

Day 29: Leanne Betasamosake Simpson
I've been sitting on Simpson for a while because there's some overlap in her writing with Robin Wall Kimmerer, and I've had a lot of different genres/styles/subjects/media I've wanted to post at least one author from. But I've now hit repeats on at least YA romance and manga, and Simpson's writing is actually quite different from Kimmerer's in a lot of ways. While Kimmerer is a biologist by training and literally braids that knowledge together with her knowledge of Potawatomi cosmology and ethics, Simpson is an Anishinaabe philosopher and anarchist, and her position as a scholar of Indigenous philosophy adds a different depth to her work: she talks in more depth about knowledge relationships and her connections with specific elders, and she has more citations to other Indigenous theorists, which is the one criticism I've ever seen of Kimmerer's work. Rather than being Indigenous and a scientist, she's Indigenous and a scholar of indigenous studies.
I've only read "Theory of Water" by Simpson, but it was excellent, and especially inspiring to read as an anarchist. Simpson's explicit politics are another difference from Kimmerer's work, which is more implicitly than explicitly political. This allows Simpson to draw extremely interesting connections to other anarchist theorists and movements. "Theory of Water" is probably a bit less accessible than "Braiding Sweetgrass," but it's richer from a theory perspective as a result.
In any case, Simpson is a magnificent writer, sharing personal insights and stories along with (and inseparable from) her theoretical ideas.
#30AuthorsNoMen

🇺🇦 Auf radioeins läuft...
Braids:
🎵 Evolution (Radio Edit)
#NowPlaying #Braids
https://braidsmusic.bandcamp.com/track/evolution
https://open.spotify.com/track/5pL1fxmM9TOGCuafSZZW0Y

On the arc index and Turaev genus of a link
\'Alvaro Del Valle V\'ilchez, Adam M. Lowrance
https://arxiv.org/abs/2509.21274 https://arxiv.org/pdf/2…

On the arc index and Turaev genus of a link
We compute the arc index of an adequate link and establish bounds on the arc index of the closure of a positive 3-braid. We also conjecture an inequality between the crossing number, arc index, and Turaev genus of a link and show the conjecture is true for several infinite families of links including alternating links, links with Turaev genus one, adequate links, closures of positive 3-braids, torus links, and most Kanenobu knots.

Braids and Beams: Exploring Fractional Statistics with Mesoscopic Anyon Colliders
Bernd Rosenow, Bertrand I. Halperin
https://arxiv.org/abs/2510.04319 https://

Braids and Beams: Exploring Fractional Statistics with Mesoscopic Anyon Colliders
Anyon colliders -- quantum Hall devices where dilute quasiparticle beams collide at a quantum point contact -- provide an interferometer-free probe of anyonic exchange phases through current cross correlations. Within a non-equilibrium bosonization framework, the normalized cross-correlations take a universal form depending only on the exchange phase and the dynamical exponent, enabling experimental demonstration of anyonic statistics. This result can be interpreted as time-domain interference …

Pointed Racks and Their Applications to Braid Theory
Angel Apollos, Jose Ceniceros
https://arxiv.org/abs/2508.03013 https://arxiv.org/pdf/2508.03013…

Pointed Racks and Their Applications to Braid Theory
We define a new algebraic structure called a \emph{pointed rack} and use it to construct ambient isotopy invariants of $ n $-braids. We first introduce an integer-valued invariant of braids using pointed racks. This is then strengthened by defining a matrix-valued invariant using racks. Moreover, our invariant determines the rack coloring invariant previously defined for the closure of the braid. Finally, we include examples of braids that are distinguished by these new invariants.

Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, Jos\'e Simental
https://arxiv.org/abs/2508.03816

Comparing cluster algebras on braid varieties
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, positroid varieties, open Bott-Samelson varieties, and Richardson varieties, among others. Recently, two cluster algebra structures were independently constructed in the coordinate rings of braid varieties: one using weaves and the other using Deodhar geometry. The main result of the article is that these two cluster alge…

Decision Theoretic Subgroup Detection With Bayesian Machine Learning
Entejar Alam, Poorbita Kundu, Antonio R. Linero
https://arxiv.org/abs/2509.05832 https://

Decision Theoretic Subgroup Detection With Bayesian Machine Learning
We consider the problem of identifying promising subpopulations in terms of treatment effectiveness or treatment effect heterogeneity, from a Bayesian decision theoretic perspective. We first show that a straight-forward application of Bayesian decision theory to subgroup detection leads to a counter-intuitive risk-seeking (RS) behavior. Motivated by this observation, we introduce the Bayesian Risk-Aware Inference and Detection of Subgroups (BRAIDS) utility and use it to perform subgroup select…

Ping-pong for basis-conjugating HNN-extension of free group
Vasily Ionin
https://arxiv.org/abs/2509.19635 https://arxiv.org/pdf/2509.19635

Ping-pong for basis-conjugating HNN-extension of free group
We construct a normal form for a multiple HNN-extension of a free group by basis-conjugating embeddings. We provide sufficient conditions on a collection of subgroups to fulfill the requirements of ping-pong lemma. Recall that the pure braid group splits as a semidirect product of free groups. Using our result, we show that certain braids from the first two summands $F_n \rtimes F_{n-1} \subset P_{n+1}$ generate a free subgroup.

Goldman-Turaev formality from the Kontsevitch integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan, Jessica Liu, Nancy Scherich
https://arxiv.org/abs/2509.20983 https://

Goldman-Turaev formality from the Kontsevitch integral
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A…

🇺🇦 #NowPlaying on #KEXP's #VarietyMix
The Braids:
🎵 Bohemian Rhapsody
#TheBraids
https://francolippi.bandcamp.com/track/the-braids-bohemian-rhapsody-franco-lippi-extended-reggaeboot-mix
https://open.spotify.com/track/3TAWWWIwm0g7PDGGL70tNn

Liftable braids and the coloured braid groupoid
Joan Licata, Vera V\'ertesi
https://arxiv.org/abs/2508.05146 https://arxiv.org/pdf/2508.05146

Liftable braids and the coloured braid groupoid
When $π:\widetildeΣ\rightarrow D^2$ is a cover of the disc branched over $n$ marked points, the braid group $B_n$ acts on the disc by homeomorphisms fixing the marked points setwise. A braid $β$ \textit{lifts} if there is a homeomorphism $\widetildeβ\in \textit{Mod}(\widetildeΣ)$ such that $β\circ π=π\circ \widetildeβ$. For arbitrary covers, the \textit{lifting homomorphism} taking $β$ to $\widetildeβ$ is only defined on a proper subgroup of the braid group. This paper extends the li…

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 …

Torsion in the Braid Monodromy of Elliptic Fibrations
Faye Jackson
https://arxiv.org/abs/2509.14454 https://arxiv.org/pdf/2509.14454

Torsion in the Braid Monodromy of Elliptic Fibrations
Given an elliptic fibration $π: M \to S^2$ with singular locus $Δ\subseteq S^2$, let $\operatorname{Br}(π) < \operatorname{Mod}(S^2,Δ)$ be the subgroup of the spherical braid group consisting of those braids that lift to a fiber-preserving diffeomorphism of $M$. We classify the order $n = |Δ|$ elements of $\operatorname{Br}(π)$ up to conjugacy in $\operatorname{Br}(π)$. To do so, we relate these conjugacy classes to special points on the $\operatorname{SL}_2$-character variety …

Determinant of the crossing matrix of a braid
Ayaka Shimizu
https://arxiv.org/abs/2509.08464 https://arxiv.org/pdf/2509.08464

Determinant of the crossing matrix of a braid
In this paper, we define a braid invariant, the purified determinant $P(b)$ of a braid $b$, considering the determinant of the crossing matrix, and show that $P(b_1 b_2)=P(b_2 b_1)$ for any pair of $n$-braids $b_1$ and $b_2$.

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Bonded braids and the Markov theorem
Paolo Cavicchioli, Bo\v{s}tjan Gabrov\v{s}ek, Matic Simoni\v{c}
…

How large is the braid monodromy of low-genus Lefschetz fibrations?
Faye Jackson
https://arxiv.org/abs/2510.04389 https://arxiv.org/pdf/2510.04389

How large is the braid monodromy of low-genus Lefschetz fibrations?
Given a genus $g$ smooth Lefschetz fibration $π: M \to S^2$ with singular locus $Δ\subseteq S^2$, we describe the subgroup $\operatorname{Br}(π)$ of the spherical braid group $\operatorname{Mod}(S^2,Δ)$ consisting of braids admitting a lift to a fiber-preserving diffeomorphism of $M$. We develop general methods for showing that the index $[\operatorname{Mod}(S^2,Δ) : \operatorname{Br}(π)]$ is infinite. As an application of our methods, we prove that $[\operatorname{Mod}(S^2,Δ) : \operato…