Geodesic
Bounding the Kirby–Thompson invariant of spun knots
Aranda, Román1 ; Pongtanapaisan, Puttipong2 ; Taylor, Scott A3 ; Zhang, Suixin (Cindy)4
1 Department of Mathematical Sciences, Binghamton University, Vestal, NY, United States, Department of Mathematics, University of Nebraska – Lincoln, Lincoln, NE, United States
2 Department of Mathematical Sciences, University of Saskatchewan, Saskatoon, SK, Canada, School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ, United States
3 Department of Mathematics, Colby College, Waterville, ME, United States
4 Department of Mathematics, University of California, Davis, Davis, CA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 6, pp. 3363-3399

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

A bridge trisection of a smooth surface in S4 is a decomposition analogous to a bridge splitting of a link in S3. The Kirby–Thompson invariant of a bridge trisection measures its complexity in terms of distances between disk sets in the pants complex of the trisection surface. We give the first significant bounds for the Kirby–Thompson invariant of spun knots. In particular, we show that the Kirby–Thompson invariant of the spun trefoil is 15.

DOI : 10.2140/agt.2024.24.3363
Keywords: bridge trisections, pants complex

Aranda, Román 1 ; Pongtanapaisan, Puttipong 2 ; Taylor, Scott A 3 ; Zhang, Suixin (Cindy) 4

1 Department of Mathematical Sciences, Binghamton University, Vestal, NY, United States, Department of Mathematics, University of Nebraska – Lincoln, Lincoln, NE, United States
2 Department of Mathematical Sciences, University of Saskatchewan, Saskatoon, SK, Canada, School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ, United States
3 Department of Mathematics, Colby College, Waterville, ME, United States
4 Department of Mathematics, University of California, Davis, Davis, CA, United States 
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Aranda, Román; Pongtanapaisan, Puttipong; Taylor, Scott A; Zhang, Suixin (Cindy). Bounding the Kirby–Thompson invariant of spun knots. Algebraic and Geometric Topology, Tome 24 (2024) no. 6, pp. 3363-3399. doi: 10.2140/agt.2024.24.3363

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