Geodesic
Shadows of 2–knots and complexity
Naoe, Hironobu1
1 Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan
Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4651-4695

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We introduce a new invariant for a 2–knot in S4, called the shadow-complexity, based on the theory of Turaev shadows, and we give a characterization of 2–knots with shadow-complexity at most 1. Specifically, we show that the unknot is the only 2–knot with shadow-complexity 0 and that there exist infinitely many 2–knots with shadow-complexity 1.

DOI : 10.2140/agt.2024.24.4651
Keywords: 2–knot, Turaev shadow, 4–manifold, complexity, banded unlink diagram

Naoe, Hironobu 1

1 Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan 
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Naoe, Hironobu. Shadows of 2–knots and complexity. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4651-4695. doi: 10.2140/agt.2024.24.4651

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