Given integers ,
we prove that there exist a collection of knots, denoted by
fulfilling the following two conditions:
(1) For any integer , there
exist infinitely many knots
(2) For any , and for
any collection of knots ,
the Heegaard genus is additive:
This implies the existence of counterexamples to Morimoto’s Conjecture [Math.
Ann. 317 (2000) 489–508].