Alexander Zupan

activity

20102024

most citedA lower bound on the width of satellite knots

10 citations · 10 across the 5 of their papers we have counts for

collaborators

5 papers

math.GT2024

Bounding the ribbon numbers of knots and links

Stefan Friedl, Filip Misev, Alexander Zupan

The ribbon number $r (K)$ of a ribbon knot $K \subset S^{3}$ is the minimal number of ribbon intersections contained in any ribbon disk bounded by $K$ . We find new lower bounds for $r…

math.GT2023

Knots bounding non-isotopic ribbon disks

Jeffrey Meier, Alexander Zupan

We exhibit infinitely many ribbon knots, each of which bounds infinitely many pairwise non-isotopic ribbon disks whose exteriors are diffeomorphic. This family provides a positive…

math.GT2023

A family of Andrews-Curtis trivializations via 4-manifold trisections

Ethan Romary, Alexander Zupan

An R-link is an $n$ -component link $L$ in $S^{3}$ such that Dehn surgery on $L$ yields $#^{n} (S^{1} \times S^{2})$ . Every R-link $L$ gives rise to a geometrically simply-connected homotop…

math.GT2023

Tri-plane diagrams for simple surfaces in $S^{4}$

Wolfgang Allred, Manuel Aragón, Zack Dooley +8

Meier and Zupan proved that an orientable surface $K$ in $S^{4}$ admits a tri-plane diagram with zero crossings if and only if $K$ is unknotted, so that the cross…

math.GT2010★ 10 cited

A lower bound on the width of satellite knots

Alexander Zupan

Thin position for knots in the 3-sphere was introduced by Gabai and has been used in a variety of contexts. We conjecture an analogue to a theorem of Schubert and Schultens concern…

Bounding the ribbon numbers of knots and links

Knots bounding non-isotopic ribbon disks

A family of Andrews-Curtis trivializations via 4-manifold trisections

Tri-plane diagrams for simple surfaces in S4

A lower bound on the width of satellite knots

Tri-plane diagrams for simple surfaces in $S^{4}$