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Destabilizing amalgamated Heegaard splittings. (English) Zbl 1216.57011
Gordon, Cameron (ed.) et al., Proceedings of the Technion workshop on Heegaard splittings, Haifa, Israel, summer 2005. Coventry: Geometry & Topology Publications. Geometry and Topology Monographs 12, 319-334 (2007).
Summary: We construct a sequence of pairs of 3-manifolds \((M_1^n,M_2^n)\) each with incompressible torus boundary and with the following two properties: (1) For \(M^n\) the result of a carefully chosen glueing of \(M_1^n\) and \(M_2^n\) along their boundary tori, the genera \((g_1^n, g_2^n)\) of \((M_1^n, M_2^n)\) and the genus \(g^n\) of \(M^n\) satisfy the inequality \(g^n/(g_1^n+ g_2^n)<1/2\). (2) The result of amalgamating certain unstabilized Heegaard splittings of \(M_1^n\) and \(M_2^n\) to form a Heegaard splitting of \(M\) produces a stabilized Heegaard splitting that can be destabilized successively \(n\) times.
For the entire collection see [Zbl 1133.57002].

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
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