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Knot exteriors with additive Heegaard genus and Morimoto's Conjecture
Tsuyoshi Kobayashi, Yo'av Rieck
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…
Knots with g(E(K)) = 2 and g(E(K#K#K)) = 6 and Morimoto's Conjecture
Tsuyoshi Kobayashi, Yo'av Rieck
We show that there exist knots K in S^3 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 (Conje…
Alexander polynomials of doubly primitive knots
Kazuhiro Ichihara, Toshio Saito, Masakazu Teragaito
We give a formula for Alexander polynomials of doubly primitive knots.
Local detection of strongly irreducible Heegaard splittings via knot exteriors
Tsuyoshi Kobayashi, Yo'av Rieck
We study the way a strongly irreducible Heegaard surface intersects a knot exterior embedded in a 3-manifold, and show that if consists of simple closed…