14 citations · 77 across the 20 of their papers we have counts for
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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…
Singular branched covers of four-manifolds
Patricia Cahn, Alexandra Kjuchukova
Consider a dihedral cover with and four-manifolds and branched along an oriented surface embedded in with isolated cone singularities. We prove that onl…
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…
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…