2007/01/26 by Tsuyoshi Kobayashi, Kobayashi, Tsuyoshi, Yo'av Rieck +2
Computer Science · Engineering · Mathematics · Medicine · #57M99 #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Orthopedic Surgery and Rehabilitation #Robotic Mechanisms and Dynamics #math.GT #msc:57M99
paper · pdf · doi:10.48550/arxiv.math/0701766
6 pages. Final version
openalex publication_date 2007/01/26 · arxiv created 2007/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that there exist knots K in S3 with g(E(K))=2 and g(E(K#K#K))=6. Together with Theorem~1.5 of [1], this proves existence of counterexamples to Morimoto's Conjecture (Conjecture 1.5 of [2]). This is a special case of arxiv.org/abs/math.GT/0701765 [1] Tsuyoshi Kobayashi and Yo'av Rieck. On the growth rate of the tunnel number of knots. J. Reine Angew. Math., 592:63--78, 2006. [2] Kanji Morimoto. On the super additivity of tunnel number of knots.Math. Ann., 317(3):489--508, 2000.