1996
DOI: 10.1016/0040-9383(95)00055-0
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Comparing Heegaard splittings of non-haken 3-manifolds

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Cited by 84 publications
(167 citation statements)
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“…(And presumably for 2-bridge links as well, though we do not pursue that here, because of the technical obstacle that the theory in [STo] so far has not been explicitly extended to 3-manifolds with non-empty boundary. Compare [RS2] to [RS1].) This result can viewed as the analogue for bridge surfaces of the result of Bonahon and Otal mentioned above.…”
Section: Introductionmentioning
confidence: 87%
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“…(And presumably for 2-bridge links as well, though we do not pursue that here, because of the technical obstacle that the theory in [STo] so far has not been explicitly extended to 3-manifolds with non-empty boundary. Compare [RS2] to [RS1].) This result can viewed as the analogue for bridge surfaces of the result of Bonahon and Otal mentioned above.…”
Section: Introductionmentioning
confidence: 87%
“…This result can viewed as the analogue for bridge surfaces of the result of Bonahon and Otal mentioned above. Our approach will be analogous to that of [RS1], working from the central result of [STo]: in the absence of incompressible Conway spheres, two c-weakly incompressible bridge surfaces can be properly isotoped to intersect in a non-empty collection of closed curves, each of which is essential (including non-meridional) in both surfaces.…”
Section: Introductionmentioning
confidence: 99%
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“…In [18], Rubinstein-Scharlemann introduced a powerful machinery, which is called a graphic, for studying Heegaard splittings of 3-manifolds, and succeeded to obtain deep results on the Reidemeister-Singer distance of two strongly irreducible Heegaard splittings of a 3-manifold. We note that Rubinstein and Scharlemann derived a graphic from two Heegaard splittings of a 3-manifold via Cerf theory [5].…”
Section: Introductionmentioning
confidence: 99%
“…In [19], Rubinstein and Scharlemann give a generalization of results in [18] for 3-manifolds with boundary. As the second application, we will give another formulation for generalizing the idea in [18] for link spaces. In fact, we will introduce an orbifold version of the Rubinstein-Scharlemann type argument(Sect.…”
Section: Introductionmentioning
confidence: 99%