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We construct a sequence of pairs of 3-manifolds (M n 1, M n 2) each with incompressible torus boundary and with the following two properties: along their 1) For M n the result of a carefully chosen gluing of M n 1 and M n 2 boundary tori, the genera (g n 1, gn 2) of (M n 1, M n 2) and the genus gn of M n satisfy the inequality g n g n 1 + gn 2 < 1 2 2) The result of amalgamating certain unstabilized Heegaard splittings of M n 1 and M n 2 to form a Heegaard splitting of M produces a stabilized Heegaard splitting that can be destabilized successively n times

Year: 2005

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