Alexander Zupan

collaborators

3 papers

math.GT2026

A homological generalized Property R conjecture is false

Tye Lidman, Trevor Oliveira-Smith, Alexander Zupan

The generalized Property R conjecture (GPRC) predicts that if framed surgery on an $n$ -component link $L$ in $S^{3}$ produces $#^{n} (S^{1} \times S^{2})$ , then $L$ is handleslide equiva…

math.GT2025

Colorings of symmetric unions and partial knots

Ben Clingenpeel, Zongzheng Dai, Gabriel Diraviam +12

Motivated by work of Kinoshita and Teraska, Lamm introduced the notion of a symmetric union, which can be constructed from a partial knot $J$ by introducing additional crossings to…

math.GT2025

Manifolds with weakly reducible genus-three trisections are standard

RomÃ¡n Aranda, Alexander Zupan

Heegaard splittings stratify 3-manifolds by complexity; only $S^{3}$ admits a genus-zero splitting, and only $S^{3}$ , $S^{1} \times S^{2}$ , and lens spaces $L (p, q)$ admit genus-one splitti…