Morse position of knots and closed incompressible surfaces

Details Morse position of knots and closed incompressible surfaces Morse position of knots and closed incompressible surfaces

2005-03-18

arxiv.org/abs/math/0503375v6

Mathematics

Geometric Topology

20 pages, 17 figures. This version (v6) is a final version to appear in J. Knot Theory and its Ramifications

Scientific paper

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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