Morse position of knots and closed incompressible surfaces

Makoto Ozawa

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Morse position of knots and closed incompressible surfaces

Makoto Ozawa

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Abstract

In this paper, we study on knots and closed incompressible surfaces in the 3-sphere via Morse functions. We show that both of knots and closed incompressible surfaces can be isotoped into a "related Morse position" simultaneously. As an application, we have following results. *Smallness of Montesinos tangles with length two and Kinoshita's theta curve *Classification of closed incompressible and meridionally incompressible surfaces in 2-bridge theta-curve and handcuff graph complements and the complements of links which admit Hopf tangle decompositions.

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BibTeX RIS

Makoto Ozawa. 2006-11-13. Morse position of knots and closed incompressible surfaces. https://arxiv.org/abs/math/0503375

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