Knot exteriors with additive Heegaard genus and Morimoto's Conjecture
| dc.creator | Kobayashi, Tsuyoshi | |
| dc.creator | Rieck, Yo'av | |
| dc.date | 2007-01-26 | |
| dc.date | 2007-01-28 | |
| dc.date.accessioned | 2026-07-07T07:43:19Z | |
| dc.date.available | 2026-07-07T07:43:19Z | |
| dc.description | Given integers g_i > 1 (i=1,...,n) we prove that there exist infinitely may knots K_i in S^3 so that g(E(K_i)) = g_i and the Heegaard genus of the exterior of the connected sum of K_1,...,K_n is the sum the Heegaard genera of K_1,...,K_n, that is: g(E(K_1#...#K_n)) = g(E(K_1)) +...+ g(E(K_n)). (Here, E() denotes the exterior and g() the Heegaard genus.) Together with Theorem 1.5 of [1], this proves the existence of counterexamples to Morimoto's Conjecture (Conjecture 1.5 of [2]). [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. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701765 | |
| dc.identifier | http://arxiv.org/abs/math/0701765 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122781 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 | |
| dc.title | Knot exteriors with additive Heegaard genus and Morimoto's Conjecture | |
| dc.type | text |