B. Bode

activity

20162026

most citedKnotted fields and explicit fibrations for lemniscate knots

47 citations · 84 across the 23 of their papers we have counts for

collaborators

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20 papers · 1 filter

math.GT2026

On T-positive links

Benjamin Bode, Paula Truöl

T-positive links form a subset of strongly quasipositive links that strictly contains the set of all non-split braid positive links. Analogous to Baader's characterisation of posit…

math.GT2026

Essential tori associated with links of mixed singularities

Raimundo N. Araújo dos Santos, Benjamin Bode, Thiago de Paiva +1

We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the exis…

math.GT2025

Mutual arc presentations and braided open books

Benjamin Bode, Chun-Sheng Hsueh

We show that every canonically fibered link in $S^{3}$ is the binding of a braided open book in $S^{3}$ , addressing a question of Montesinos and Morton. We introduce mutual arc present…

math.GT2024

Totally tangential $C$ -links and electromagnetic knots

Benjamin Bode

The set of real-analytic Legendrian links with respect to the standard contact structure on the 3-sphere $S^{3}$ corresponds both to the set of totally tangential $C$ -links…

math.GT2024

Complex optical vortex knots

Benjamin Bode

The curves of zero intensity of a complex optical field can form knots and links: optical vortex knots. Both theoretical constructions and experiments have so far been restricted t…

math.GT2024

Ultraknots and limit knots

Benjamin Bode

We prove that every knot type in $R^{3}$ can be parametrised by a smooth function $f : S^{1} \to R^{3}$ , $f (t) = (x (t), y (t), z (t))$ such that all derivatives $f^{(n)}(t)=(x^{(…

math.GT2023

Links of inner non-degenerate mixed functions, Part II

Benjamin Bode

Let $f : C^{2} \to C$ be an inner non-degenerate mixed polynomial with a nice Newton boundary with $N$ compact 1-faces. In the first part of this series of papers we sh…

math.GT2022★ 1 cited

Closures of T-homogeneous braids are real algebraic

Benjamin Bode

A link in $S^{3}$ is called real algebraic if it is the link of an isolated singularity of a polynomial map from $R^{4}$ to $R^{2}$ . It is known that every real algebra…

math.GT2022★ 1 cited

All links are semiholomorphic

Benjamin Bode

Semiholomorphic polynomials are functions $f : C^{2} \to C$ that can be written as polynomials in complex variables $u$ , $v$ and the complex conjugate $v$ . W…

math.GT2022★ 3 cited

Links of singularities of inner non-degenerate mixed functions

Raimundo N. Araújo dos Santos, Benjamin Bode, Eder L. Sanchez Quiceno

We introduce the notion of a (strongly) inner non-degenerate mixed function $f : C^{2} \to C$ . We show that inner non-degenerate mixed polynomials have weakly isolated…

math.GT2021

Braided open book decompositions in $S^{3}$

Benjamin Bode

We study four (a priori) different ways in which an open book decomposition of the 3-sphere can be defined to be braided. These include generalised exchangeability defined by Morto…

math.GT2020★ 2 cited

Twisting and satellite operations on P-fibered braids

Benjamin Bode

A geometric braid $B$ can be interpreted as a loop in the space of monic complex polynomials with distinct roots. This loop defines a function $g : C \times S^{1} \to C$ …

math.GT2020

Knotted surfaces as vanishing sets of polynomials

Benjamin Bode, Seiichi Kamada

We present an algorithm that takes as input any element $B$ of the loop braid group and constructs a polynomial $f : R^{5} \to R^{2}$ such that the intersection of the va…

math.GT2019

Quasipositive links and electromagnetism

Benjamin Bode

For every link $L$ we construct a complex algebraic plane curve that intersects $S^{3}$ transversally in a link $L ~$ that contains $L$ as a sublink. This construction proves t…

math.GT2019

Real algebraic links in $S^{3}$ and braid group actions on the set of $n$ -adic integers

Benjamin Bode

We construct an infinite tower of covering spaces over the configuration space of $n - 1$ distinct non-zero points in the complex plane. This results in an action of the braid group…

math.GT2017

Crossing numbers of composite knots and spatial graphs

Benjamin Bode

We study the minimal crossing number $c (K_{1} # K_{2})$ of composite knots $K_{1} # K_{2}$ , where $K_{1}$ and $K_{2}$ are prime, by relating it to the minimal crossing number of spatia…

math.GT2017

Constructing links of isolated singularities of polynomials $R^{4} \to R^{2}$

Benjamin Bode

We show that if a braid $B$ can be parametrised in a certain way, then previous work can be extended to a construction of a polynomial $f : R^{4} \to R^{2}$ with the clos…

math.GT2016★ 5 cited

Constructing a polynomial whose nodal set is any prescribed knot or link

Benjamin Bode, Mark R. Dennis

We describe an algorithm that for every given braid $B$ explicitly constructs a function $f : C^{2} \to C$ such that $f$ is a polynomial in $u$ , $v$ and $\ove…

math.GT2016★ 17 cited

Constructing a polynomial whose nodal set is the three-twist knot $5_{2}$

Mark R Dennis, Benjamin Bode

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_{2}$ . The construction g…

math.GT2016★ 47 cited

Knotted fields and explicit fibrations for lemniscate knots

Benjamin Bode, Mark R Dennis, David Foster +1

We give an explicit construction of complex maps whose nodal line have the form of lemniscate knots. We review the properties of lemniscate knots, defined as closures of braids whe…

On T-positive links

Essential tori associated with links of mixed singularities

Mutual arc presentations and braided open books

Totally tangential C-links and electromagnetic knots

Complex optical vortex knots

Ultraknots and limit knots

Links of inner non-degenerate mixed functions, Part II

Closures of T-homogeneous braids are real algebraic

All links are semiholomorphic

Links of singularities of inner non-degenerate mixed functions

Braided open book decompositions in S3

Twisting and satellite operations on P-fibered braids

Knotted surfaces as vanishing sets of polynomials

Quasipositive links and electromagnetism

Real algebraic links in S3 and braid group actions on the set of n-adic integers

Crossing numbers of composite knots and spatial graphs

Constructing links of isolated singularities of polynomials R4→R2

Constructing a polynomial whose nodal set is any prescribed knot or link

Constructing a polynomial whose nodal set is the three-twist knot 52​

Knotted fields and explicit fibrations for lemniscate knots

Totally tangential $C$ -links and electromagnetic knots

Braided open book decompositions in $S^{3}$

Real algebraic links in $S^{3}$ and braid group actions on the set of $n$ -adic integers

Constructing links of isolated singularities of polynomials $R^{4} \to R^{2}$

Constructing a polynomial whose nodal set is the three-twist knot $5_{2}$