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Morse position of knots and closed incompressible surfaces

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In this talk, we show that we can isotope a closed incompressible surface to a good position in the complement of a knot placed in a Morse position. Then as an application, we have following results.

  1. Smallness of Montesinos tangles
  2. Classification of closed incompressible and meridionally incompressible surfaces in 2-bridge theta-curve or handcuff graph complements

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e-mail: [email protected], [email protected]

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