Alternation Numbers of Torus Knots with Small Braid Index

作者：Feller Peter^*; Pohlmann Simon; Zentner Raphael

来源：Indiana University Mathematics Journal, 2018, 67(2): 645-655.

DOI：10.1512/iumj.2018.67.7302

• Torus knots
• alternation number
• alternating number
• dealternating number
• upsilon-invariant

We calculate the alternation number of torus knots with braid index 4 and less. For the lower bound, we use the Upsilon-invariant recently introduced by Ozsvath, Stipsicz, and Szabo. For the upper bound, we use a known bound for braid index 3 and a new bound for braid index 4. Both bounds coincide, so that we obtain a sharp result.

• 出版日期2018