Alexandra Kjuchukova

activity

20162026

most citedWirtinger systems of generators of knot groups

14 citations · 77 across the 20 of their papers we have counts for

collaborators

21 papers

math.GT2026

Cobordism groups of dihedral branched covers

Valentina Bais, Alexandra Kjuchukova

For every integer $n \geq 1$ , we compute the cobordism groups of dihedral $n$ -fold branched covers of $S^{3}$ with oriented and non-oriented branching sets. We show that the groups a…

math.GT2026

Extending Quotients of Knot Groups over Surfaces in $B^{4}$

Alexandra Kjuchukova, Kent E. Orr

Let $K \subseteq S^{3}$ be a knot with exterior $E_{K}$ , and denote by $ρ : π_{1} (E_{K}) ↠ G$ a quotient of its group. We give a sharp obstruction to the existence of a…

math.GT2025

Branched Covers of Open Manifolds

Mark Hughes, Alexandra Kjuchukova, Maggie Miller

For $m = 2$ and $m = 3$ we prove that any connected, oriented, open manifold $M^{m}$ admits a simple branched covering map over $R^{m}$ . When $M$ has $k$ ends and $k$ is finite, t…

math.GT2025

The Plain Sphere Number of a Link

Ryan Blair, Alexandra Kjuchukova, Ella Pfaff

Let $L$ be a link in $S^{3}$ . We consider the class of meridional presentations for $π_{1} (S^{3} \ L)$ in which the relations are witnessed by embedded two-spheres which can be r…

math.GT2024

Adding a suitable unknot to any link equates bridge number and meridional rank

Ryan Blair, Alexandra Kjuchukova, Ella Pfaff

Given any link $L \subseteq S^{3}$ , we show that it is possible to embed an unknot $U$ in its complement so that the link $L \cup U$ satisfies the Meridional Rank Conjecture (MRC). The…

math.GT2023

Linking in Cyclic Branched Covers and Satellite (non)-Homomorphisms

Patricia Cahn, Alexandra Kjuchukova

Let $K \subset S^{3}$ be a knot and $η, γ \subset S^{3} \ K$ be simple closed curves. Denote by $Σ_{q} (K)$ the $q$ -fold cyclic branched cover of $K$ . We give an explicit formula fo…

math.GT2022

Coxeter quotients of knot groups through 16 crossings

Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison

We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Capp…

math.GT2021★ 2 cited

Slicing knots in definite 4-manifolds

Alexandra Kjuchukova, Allison N. Miller, Arunima Ray +1

We study the $CP^{2}$ -slicing number of knots, i.e. the smallest $m \geq 0$ such that a knot $K \subseteq S^{3}$ bounds a properly embedded, null-homologous disk in a punctured…

math.GT2021

Brunnian exotic surface links in the 4-ball

Kyle Hayden, Alexandra Kjuchukova, Siddhi Krishna +3

This paper investigates the exotic phenomena exhibited by links of disconnected surfaces with boundary that are properly embedded in the 4-ball. Our main results provide two differ…

math.GT2020★ 4 cited

The bridge number of arborescent links with many twigs

Sebastian Baader, Ryan Blair, Alexandra Kjuchukova +1

We prove the meridional rank conjecture for arborescent links associated to plane trees with the following property: all branching points carry a straight branch to at least three…

math.GT2019

A note on three-fold branched covers of $S^{4}$

Ryan Blair, Patricia Cahn, Alexandra Kjuchukova +1

We show that any 4-manifold admitting a $(g; k_{1}, k_{2}, 0)$ -trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^{4}$ , smoothly embedded except…

math.GT2019★ 11 cited

Average four-genus of two-bridge knots

Sebastian Baader, Alexandra Kjuchukova, Lukas Lewark +2

We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.

math.GT2019★ 3 cited

Signatures of topological branched covers

Christian Geske, Alexandra Kjuchukova, Julius L. Shaneson

Let $X^{4}$ and $Y^{4}$ be smooth manifolds and $f : X \to Y$ a branched cover with branching set $B$ . Classically, if $B$ is smoothly embedded in $Y$ , the signature $σ (X)$ can be comput…

math.GT2018★ 3 cited

The Dihedral Genus of a Knot

Patricia Cahn, Alexandra Kjuchukova

Let $K \subset S^{3}$ be a Fox $p$ -colored knot and assume $K$ bounds a locally flat surface $S \subset B^{4}$ over which the given $p$ -coloring extends. This coloring of $S$ induces a d…

math.GT2018★ 1 cited

Computing Ribbon Obstructions for Colored Knots

Patricia Cahn, Alexandra Kjuchukova

Kjuchukova's $Ξ_{p}$ invariant gives a ribbon obstruction for Fox $p$ -colored knots. The invariant is derived from dihedral branched covers of 4-manifolds, and is needed to calculate…

math.GT2017★ 8 cited

Symmetric quotients of knot groups and a filtration of the Gordian graph

Sebastian Baader, Alexandra Kjuchukova

We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups s…

math.GT2017★ 9 cited

Singular branched covers of four-manifolds

Patricia Cahn, Alexandra Kjuchukova

Consider a dihedral cover $f : Y \to X$ with $X$ and $Y$ four-manifolds and $f$ branched along an oriented surface embedded in $X$ with isolated cone singularities. We prove that onl…

math.GT2017★ 3 cited

The incompatibility of crossing number and bridge number for knot diagrams

Ryan Blair, Alexandra A. Kjuchukova, Makoto Ozawa

We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior o…

math.GT2017★ 14 cited

Wirtinger systems of generators of knot groups

Ryan Blair, Alexandra Kjuchukova, Roman Velazquez +1

We define the {\it Wirtinger number} of a link, an invariant closely related to the meridional rank. The Wirtinger number is the minimum number of generators of the fundamental gro…

math.GT2016★ 8 cited

Linking Numbers in Three-Manifolds

Patricia Cahn, Alexandra Kjuchukova

Let $M$ be a connected, closed, oriented three-manifold and $K$ , $L$ two rationally null-homologous oriented simple closed curves in $M$ . We give an explicit algorithm for computin…

math.GT2016★ 11 cited

Dihedral branched covers of four-manifolds

Alexandra Kjuchukova

Given a closed oriented PL four-manifold $X$ and a closed surface $B$ embedded in $X$ with isolated cone singularities, we give a formula for the signature of an irregular dihedral…

Cobordism groups of dihedral branched covers

Extending Quotients of Knot Groups over Surfaces in B4

Branched Covers of Open Manifolds

The Plain Sphere Number of a Link

Adding a suitable unknot to any link equates bridge number and meridional rank

Linking in Cyclic Branched Covers and Satellite (non)-Homomorphisms

Coxeter quotients of knot groups through 16 crossings

Slicing knots in definite 4-manifolds

Brunnian exotic surface links in the 4-ball

The bridge number of arborescent links with many twigs

A note on three-fold branched covers of S4

Average four-genus of two-bridge knots

Signatures of topological branched covers

The Dihedral Genus of a Knot

Computing Ribbon Obstructions for Colored Knots

Symmetric quotients of knot groups and a filtration of the Gordian graph

Singular branched covers of four-manifolds

The incompatibility of crossing number and bridge number for knot diagrams

Wirtinger systems of generators of knot groups

Linking Numbers in Three-Manifolds

Dihedral branched covers of four-manifolds

Extending Quotients of Knot Groups over Surfaces in $B^{4}$

A note on three-fold branched covers of $S^{4}$