| 
          
            | Abstract |  
            | We  introduce  a  new  invariant  for  a
 
–knot in
 
, called the
 shadow-complexity, based on the theory of Turaev shadows, and we give a characterization of
 
–knots with
 shadow-complexity at most 
.
 Specifically, we show that the unknot is the only
 
–knot with shadow-complexity
 
 and that there exist
 infinitely many 
–knots
 with shadow-complexity 
.
  |  
          
            | Keywords
                2–knot, Turaev shadow, 4–manifold, complexity, banded
                unlink diagram
               |  
          
            | Mathematical Subject Classification
                Primary: 57K40, 57K45
               
                Secondary: 57R65
               |  
          
            | Publication
                Received: 9 November 2022
               
                Revised: 9 May 2023
               
                Accepted: 2 August 2023
               
                Published: 17 December 2024
               |  
          
            | © 2024 MSP (Mathematical Sciences
            Publishers). Distributed under the Creative Commons
            Attribution License 4.0 (CC BY). |  Open Access made possible by participating
        institutions via Subscribe to Open.   |