Alexandra Kjuchukova

activity

20172026

most citedSingular branched covers of four-manifolds

9 citations · 9 across the 2 of their papers we have counts for

collaborators

7 papers

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.GT2019

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

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…