Year: 2026
Type: preprint
Abstract: A {\em shadow} (or {\em projection}) is obtained from a link diagram by ignoring the over/under information at each crossing. Given a fixed link $L$ we investigate the complexity of deciding whether an input shadow $S$ can be {\em resolved} into $L$, that is, whether we can assign over/under information to its crossings to obtain a diagram of a link isotopic to $L$. We show that if $L\in\{3_1,4_1,5_1,5_2,6_2,L2a1, L4a1, L5a1, L6n1\}$ then there exists a linear-time algorithm that decides whether an input shadow $S$ resolves into $L$.
Source: arXiv (Cornell University)
Authors: Alba, Andrea, Salazar, Gelasio
Institution: Autonomous University of San Luis Potosí
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203945867
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